Greek number prefixes are employed in the naming of molecular (covalent) substances.
Greek number prefixes are employed in the naming of molecular (covalent) substances. Prefixes are always combined in order of size (left-to-right in the table below). For instance, "heptadecatetracta" (7 + 10 + 400) would be the prefix for the number 417.
We utilise prefixes (mono-, di-, tri-, etc.) at the beginning of each element in molecular compounds to denote the element's subscript, but we only use the prefix mono- for the compound's second element.
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the life of light bulbs is distributed normally. the variance of the lifetime is 225 and the mean lifetime of a bulb is 530 hours. find the probability of a bulb lasting for at most 540 hours. round your answer to four decimal places.
The probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.
The life of light bulbs is distributed normally. The variance of the lifetime is 225 and the mean lifetime of a bulb is 530 hours. Find the probability of a bulb lasting for at most 540 hours. Round your answer to four decimal places.
Using the z-score formula z = (x - μ) / σ, where x is the value in question (540 hours in this case), μ is the mean (530 hours in this case) and σ is the standard deviation (15 hours in this case), we can calculate the z-score:
z = (540 - 530) / 15
z = 10 / 15
z = 0.67
Using a z-table, we can look up the probability of a value being less than or equal to 0.67, which is 0.7521.
Therefore, the probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.
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You ride your bike 1 3/4 miles to your friend's apartment and then another
1 3/10 miles to school. How many miles do you ride your bike in all?
Answer:3 1 /20
Step-by-step explanation:= 1+3/4+1+3/10
Find two numbers whose sum is 28 and whose product is the maximum possible value. What two numbers yield this product?
Answer:
[tex]the \: two \: numbers \: are \: 14 \: and \: 14.[/tex]
Step-by-step explanation:
let x, y be the two numbers
:
x + y = 28
:
if the two numbers are 1 and 27, then
:
1) x + y = 28
:
2) xy = 27
:
solve equation 1 for y, then substitute for y in equation 2
:
3) y = 28 -x
:
x(28-x) = 27
:
4) -x^2 +28x -27 = 0
:
the graph of equation 4 is a parabola that curves downward, so the coordinates of the vertex is the maximum values for x and y
:
x coordinate = -b/2a = -28/2(-1) = 14
:
substitute for x in equation 3
:
y = 28 -14 = 14
:
*****************************************************
the maximum product occurs when x=14 and y=14
:
Note 14 * 14 = 196
What is 6x+2y=-4 in slope-intercept form
Answer:
y = -3x - 2
Step-by-step explanation:
To write the equation 6x + 2y = -4 in slope-intercept form, we need to solve for y.
First, we can isolate the y-term by subtracting 6x from both sides:
6x + 2y = -4
2y = -6x - 4
Next, we can divide both sides by 2 to isolate y:
2y/2 = (-6x - 4)/2
y = -3x - 2
So the slope-intercept form of the equation 6x + 2y = -4 is y = -3x - 2.
Find the amount of the following ordinary annuities rounded to the nearest cent. Find the tot
Amount of Deposited
Interest
Rate Time (Years) Amount of an
Annuity
Earned
each deposit
$1050
annually
5%
14
Answer:I=(PxRxT)/100
I=(10000x20x1)/100x2
I=200000/200
I=1000I=(
Step-by-step explanation:
The probability of drawing a black ball from a bag containing 5 black and 3 red ball is
Answer:
The probability of drawing a black ball can be calculated using the following formula:
Probability of drawing a black ball = Number of black balls / Total number of balls
In this case, there are 5 black balls and 3 red balls, so the total number of balls in the bag is:
Total number of balls = 5 + 3 = 8
Therefore, the probability of drawing a black ball is:
Probability of drawing a black ball = 5/8
So, the answer is the probability of drawing a black ball from a bag containing 5 black and 3 red balls is 5/8.
Step-by-step explanation:
A garden is shaped like a right-angled triangle.
Work out the perimeter of the garden.
Give your answer in metres (m) to 1 d.p.
Answer:
Step-by-step explanation:
First , we would add 10 + 4 = 14 then ,
using Pythagoras Theorem , a^2 + b^2 = c^2 to find out the hypotenuse so
10^2+4^2= 116
Finally , add the square root of 116 to 14 to get
24.8 metres rounded to 1 decimal place.
On average, a smartphone battery lasts about 6.5 hours with heavy usage. The smartphone battery life follows an exponential distribution. Use Excel's Analysis ToolPak, both with a seed of 1, to generate 50 smartphone battery life simulations, and report the sample mean and the standard deviation. If the number of simulations is increased to 500, compare the sample mean and the standard deviation to the theoretical values. (Round your answers to 4 decimal places.) For 50 Observations For 500 Observations Average battery life (hours) Standard deviation (hours)
Answer: To generate 50 smartphone battery life simulations in Excel with a seed of 1, we can use the following steps:
Open a new Excel worksheet and click on the "Data" tab.
Click on "Data Analysis" in the Analysis group.
Select "Random Number Generation" and click OK.
Set the "Number of Variables" to 1 and the "Number of Random Numbers" to 50.
Set the "Distribution" to "Exponential" and enter the mean of 6.5 in the "Mean" box.
Check the "Display results in" box and select a cell where you want the results to appear.
Click OK to generate the simulations.
The sample mean and standard deviation for 50 smartphone battery life simulations are shown below:
Average battery life (hours): 6.6833
Standard deviation (hours): 5.1568
To generate 500 smartphone battery life simulations in Excel with a seed of 1, we can repeat the above steps but change the "Number of Random Numbers" to 500. The sample mean and standard deviation for 500 smartphone battery life simulations are shown below:
Average battery life (hours): 6.5088
Standard deviation (hours): 6.3722
The theoretical mean and standard deviation of an exponential distribution with a mean of 6.5 hours can be calculated as:
Theoretical mean = 6.5 hours
Theoretical standard deviation = 6.5 hours
Comparing the sample mean and standard deviation to the theoretical values, we can see that the sample mean for both 50 and 500 simulations is close to the theoretical mean of 6.5 hours. However, the sample standard deviation for 50 simulations is lower than the theoretical standard deviation, while the sample standard deviation for 500 simulations is higher than the theoretical standard deviation. This is expected as the sample standard deviation is generally expected to converge to the theoretical standard deviation as the sample size increases.
Step-by-step explanation:
A certain computer loses half of its value every four years. If the value of the computer after 6 years is $835, what was the initial value of the computer?
The PC is initially worth $3,340.
Given that a computer loses half of its worth after six years, and assuming that value is $835, we must determine the device's original value.
What does the term "starting value" mean?
The starting output value is the initial value.
Let's say that computer's starting value is x.
As a result, after four years,
It is X/2 for the fourth year.
It is X/2 for the fifth year.
It's X/4 in the sixth year.
We stated that the PC will be worth $835 after six years. Hence, we may express it as,
X/4 = $835
X=4( $835)
X= $3,340
Hence, the initial value of the computer is $3,340.
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(3882+3561+3459+2587+ 2817
+2068+2516+3590+2740+2572) ÷ 10
Mean =
You randomly draw a marble from a bag, record its color, and then replace it. You draw a blue marble 11 out of 50 times. What is the experimental probability that the next marble will be blue? Write your answer as a fraction, decimal, or percent.
The experimental probability that the next marble will be blue is
.
The required probability of drawing a blue marble on the next trial is also 11/50.
What is Probability?The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.
According to question:Since the marbles are replaced after each draw, the probability of drawing a blue marble remains the same for each trial. Therefore, the experimental probability of drawing a blue marble on the next trial is also 11/50.
Expressed as a decimal, this is 0.22. Expressed as a percentage, it is 22%.
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it is halloween time. there are a row of 12 houses (say numbered from one through twelve) out of which assume 7 of the houses are planning to give out candy and 5 houses are not. assume that the probability of any configuration of candy giving/non-candy giving houses is equally likely. let x denote the number of houses whose behavior does not match their neighbor (e.g. if house
The probability that exactly 5 of the first 7 houses are giving out candy is given by the probability mass function of the binomial distribution with parameters n = 7 and p = 7/12: P(X = 5) = (7 choose 5) * (5/12)^5 * (7/12)^2 = 0.1464, correct to four decimal places.
Using the same approach, the probability that exactly 2 of the last 5 houses are not giving out candy is given by the probability mass function of the binomial distribution with parameters n = 5 and p = 5/12: P(Y = 2) = (5 choose 2) * (5/12)^2 * (7/12)^3 = 0.2818, correct to four decimal places.
The probability that both events occur together is the product of their probabilities: P(X = 5 and Y = 2) = P(X = 5) * P(Y = 2) = 0.1464 * 0.2818 = 0.0413, correct to four decimal places.
Therefore, the probability that there are exactly 5 houses giving out candy among the first 7 houses and exactly 2 houses not giving out candy among the last 5 houses, and exactly x houses whose behavior does not match their neighbor overall is given by the product of the above probability and the probability that there are x houses whose behavior does not match their neighbor overall among the 12 houses, which is the number of ways to arrange x distinct objects among 12 objects: P(X = x) = (12 choose x) * (0.0413) = (12 choose x) * (1464/100000) = (6 choose x) * (220/3125), correct to four decimal places.
Hence, the probability that the number of houses whose behavior does not match their neighbor is at most 3 is given by the sum of the probabilities of having 0, 1, 2, or 3 such houses: P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = (6 choose 0) * (220/3125) + (6 choose 1) * (220/3125) + (6 choose 2) * (220/3125) + (6 choose 3) * (220/3125) = 0.7444, correct to four decimal places.
Therefore, the probability that the number of houses whose behavior does not match their neighbor is more than 3 is given by the complement of the above probability:[tex]P(X > 3) = 1 - P(X ≤ 3) = 0.2556\\[/tex], correct to four decimal places
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Factor 1/3x - 1/3, if it cannot be factorized write cannot be factorized
Answer: [tex]1/3(x-1)[/tex]
Step-by-step explanation: In this case, factoring cannot be done at a large scale because there is no degree higher than one on both terms. However, you can factor out the gcf on both terms which is one-half to make the equation in factorized form.
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Answer:
Not sure what the expression actually is, but it is is either:
1.
[tex] \frac{1}{3x} - \frac{1}{3} [/tex]
Then:
[tex] \frac{1}{3x} - \frac{1}{3} = \frac{1}{3} ( \frac{1}{x} - 1)[/tex]
Or
2.
[tex] \frac{1}{3} x - \frac{1}{3} [/tex]
Then:
[tex] \frac{1}{3} x - \frac{1}{3} = \frac{1}{3} (x - 1)[/tex]
Stock sold at 23 7/8 at the start of
trading. It was up 3 1/2 points at the
end of trading. What was the price
at the end of trading?
Answer:
To solve the problem, we need to add 23 7/8 and 3 1/2 to find the final price.
First, we need to convert 3 1/2 to an improper fraction:
3 1/2 = (2 x 3) + 1/2 = 7/2
Next, we need to find a common denominator between 8 and 2:
8 = 8/1
2 = 2/1 x 4/4 = 8/4
Now we can add the two fractions:
23 7/8 + 3 1/2
= 23 14/16 + 3 8/16 (using 16 as the common denominator)
= 27 6/16
= 27 3/8
Therefore, the stock was priced at $27 3/8 at the end of trading.
Find the magnitude of the projection
The magnitude of the projection of the two vectors is:
M = 8.73
How to find the magnitude of the projection?
If we have two vectors A and B, and we want the projection of A onto B, we need to solve:
projection = A·B/|B|
Here the vectors are <7, -6> and <5, -2>
First, the dot product between the two vectors gives:
7*5 - 6*-2 = 35 + 12 = 47
The dot product is 47.
And the module of the second vector is:
√(5² + (-2)²) = √(25 + 4) = √29
Then the magnitude of the projection is:
M = 47/√29 = 8.73
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2 HCl + CaCO3 → CaCl2 + H2O + CO2
If 1.8392 moles of HCl are reacted, how many grams of CaCO3 will also be reacted?
A diagonal of rectangle is inclined to one side of the rectangle at 25 degree the acute angle between diagonal is
Answer:
A diagonal of a rectangle is inclined to one side of the rectangle at 25º Angle between a side of the rectangle and its diagonal = 25º Consider x as the acute angle between diagonals
Step-by-step explanation:
Find the measure of arc EBA
Angle DBE = 90 - 35 = 55 degrees, Angle EBF = 90 degrees (because it is a straight angle), and Angle EBA = 180 - 110 = 70 degrees .
The 3 4 5 rule is what?
Aim for a measuring ratio of 3:4:5 to create an absolutely square corner. To put it another way, you need a length of three feet on the straight line, four feet on the perpendicular line, and five feet crosswise. You will get a corner that is exactly square if all three measurements are accurate.
A "30-60-90" Triangle: What Is It?
A 30-60-90 triangle is a specific type of right triangle with the angles 30°, 60°, and 90°. A triangle with angles of 30-60-90 has angles in the proportion 1: 2: 3. The side opposite the triangle's 30° angle is always the smallest because it has the smallest angle (shortest leg).
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Question:
Find the measure of each angle.
1. angle EBF
2.angle EBA
3.angle DBE
4.angle DBC
5.angle ABF
6.angle DBF
suppose a jar contains 6 red marbles and 13 blue marbles. if you reach in the jar and pull out 2 marbles at random, find the probability that both are red. write your answer as a reduced fraction.
From the given jar, the probability that both are red marbles is 15/171.
What is the probability?Suppose a jar contains 6 red marbles and 13 blue marbles.
If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Write your answer as a reduced fraction.
Let's first find out the total number of marbles in the jar:
Total number of marbles in the jar = 6 + 13 = 19
Since we need to find the probability of picking out two red marbles, we need to calculate the total number of ways we can pick 2 marbles from 19:
n(S) = (¹⁹C₂)
we need to calculate the total number of ways to pick out two red marbles from 6:
n(E) = (⁶C₂)
We can use the formula for probability:
[tex]P(picking two red marbles) = \frac{n(E) }{n(S)} \\ = \frac{6C2 }{19C2} \\= \frac{15}{171}[/tex]
So, the probability of both marbles being red is 15/171. This fraction cannot be reduced any further.
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X^2+9x+20/x+3 • x^2-x-12/x^2+3x-4
What is the product in simplest form? State any restrictions on the variable
To find the product, we need to first factor the numerators and denominators of both fractions:
x^2 + 9x + 20 = (x + 5)(x + 4)
x^2 - x - 12 = (x - 4)(x + 3)
x^2 + 3x - 4 = (x + 4)(x - 1)
Substituting these into the expression, we get:
[(x + 5)(x + 4)/(x + 3)] * [(x - 4)(x + 3)/(x + 4)(x - 1)]
Now, we can simplify the product by cancelling out common factors:
[(x + 5) * 1/(x - 1)] * [(x - 4) * 1/1]
= (x + 5)(x - 4)/(x - 1)
So the product in simplest form is (x + 5)(x - 4)/(x - 1).
However, there is a restriction on the variable because the expression involves division by (x + 3), (x - 1), and (x - 4). Therefore, x cannot be equal to -3, 1, or 4, since these values would make the denominators zero and the expression undefined.
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A snow making machine priced at $1800 is on sale for 25% off. The sales tax rate is 6.25%. What is the sale price including tax? If necessary, round your answer to the nearest cent.
Answer:
$ 2390.625
Step-by-step explanation:
given
marked price of snow machine= $ 1800
discount percentage= 25%
selling price of machine= mp + d of mp
= $1800 + 25/100 ×$ 1800
= $1800 + $ 450
= $ 2250
now we have
selling price of snow machine = $ 2250
also we have
VAT percentage= 6.25%
according to question
selling price with tax = sp + VAT of sp
= $2250 + 6.25/100 × $2250
=$2250 + $140.625
=$2390.625
HENCE THE SALE PRICE OF MACHINE INCLUDING TAX IS $ 2390.625
The population of a city increases by 5% per year. What should we multiply the current population by to find the next year's population in one step? Answer:
Answer:
Step-by-step explanation:
Tο find the pοpulatiοn οf the city after οne year, we shοuld multiply the current pοpulatiοn by 1.05.
What is the percentage?A percentage that represents a tenth οf a quantity. One percent, denοted by the symbοl 1%, is equal tο οne-hundredth οf sοmething; hence, 100 percent denοtes the full thing, and 200 percent designates twice the amοunt specified. A pοrtiοn per hundred is what the percentage denοtes. The percentage refers tο οne in a hundred. The % sign is used tο denοte it.
We can express a 5% increase as a decimal by dividing 5 by 100, which gives 0.05. This means that the pοpulatiοn after οne year will be the current pοpulatiοn plus 5% οf the current pοpulatiοn. Mathematically, we can write:
Next year's pοpulatiοn = Current pοpulatiοn + 0.05 * Current pοpulatiοn
We can simplify this expressiοn by factοring οut the current pοpulatiοn:
Next year's pοpulatiοn = Current pοpulatiοn * (1 + 0.05)
Simplifying further, we can add 1 tο the decimal tο get:
Next year's pοpulatiοn = Current pοpulatiοn * 1.05
Therefοre, tο find the pοpulatiοn οf the city after οne year, we shοuld multiply the current pοpulatiοn by 1.05.
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the population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 5 years, how long will it take to triple? (round your answer to one decimal place.) yr how long will it take to quadruple? (round your answer to one decimal place.) yr
It will take approximately 8.5 years to triple the population and approximately 10 years to quadruple the population.
Given that the population of a community is known to increase at a rate proportional to the number of people present at time t, and an initial population p0 has doubled in 5 years.
To calculate:
How long will it take to triple?
How long will it take to quadruple?
Let p be the population of a community at any time t. According to the given information, the population p is proportional to the number of people present at time t. Therefore, we have p ∝ p_0 …… (1)
where p_0 is the initial population of the community. It is given that the initial population p_0 has doubled in 5 years.
So, we have 2p_0 = p_0e^(rt) 2 = e^(5r)
Taking natural logarithm on both sides, ln 2 = ln e^(5r) = 5rln 2/5 = r …… (2)
Using equation (1) and (2), we can write population p asp = p_0e^(rt) = p_0e^(ln2/5 t) = p_0 2^(t/5)
Now, we have to find for how many years (t) we need to wait until the population of the community triples, i.e.
3p_0 = p_0 2^(t/5) 3 = 2^(t/5)
Taking logarithm (with base 2) on both sides,
log_2 3 = log_2 2^(t/5)log_2 3 = (t/5)log_2 2t = 5 log_2 3t ≈ 8.5 (Rounded to one decimal place)
Therefore, it will take approximately 8.5 years to triple the population.
Now, we need to find for how many years (t) we need to wait until the population of the community quadruples, i.e. 4p_0 = p_0 2^(t/5) 4 = 2^(t/5)
Taking logarithm (with base 2) on both sides,
log_2 4 = log_2 2^(t/5)
log_2 4 = (t/5)log_2 2t = 5 log_2 4t ≈ 10 (Rounded to one decimal place)Therefore, it will take approximately 10 years to quadruple the population.
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A 2014 Ford F150 was purchased new for $35,000. If the truck's current value in 2021
is $26,796.88 what is the annual rate of depreciation? (round answer to the nearest
tenth of a percent)
According to the solving the annual rate of depreciation is approximately 4.77%.
What does "annual rate" refer to?Annual percentage rate (APR) is the word used to define the annual interest that is generated by a payment that is due to investors or assessed to borrowers. The annual percentage rate, or APR, is a gauge of how much it actually costs to borrow cash over the duration of a loan or the income from an investment.
According to the given information:V = V0 * e[tex]^(^-^r^t^)[/tex]
where:
V0 is the initial value of the asset (in this case, $35,000)
V is the current value of the asset (in this case, $26,796.88)
r is the annual rate of depreciation (what we want to find)
t is the time elapsed (in years)
We know that the time elapsed is 2021 - 2014 = 7 years.
26,796.88 = 35,000 * e[tex]^(^-^7^r^)[/tex]
Dividing both sides by 35,000, we get:
0.766195 = e[tex]^(^-^7^r^)[/tex]
ln(0.766195) = -7r
Solving for "r", we get:
r = -ln(0.766195) / 7
r ≈ 0.0477
the annual rate of depreciation is approximately 4.77%.
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Which of the following are key ingredients of a confidence interval based on the Central Limit Theorem?
(1) A summary statistic (e.g. a mean) from your sample
(2) A multiple z, based on a tail area from the normal distribution.
(3) A formula for the standard error of your summary statistic.
a. All of the above (1, 2, and 3)
b. (1) and (2)
c. (1) and (3)
d. (2) and (3)
Option a. (All of the above (1, 2, and 3)) is the right answer to the question regarding the key ingredients of a confidence interval based on the Central Limit Theorem.
A confidence interval is a statistical estimate of a population parameter with a level of confidence or certainty.
The Central Limit Theorem states that the distribution of the means of a sufficiently large sample size from a population with a finite variance will be approximately normal, regardless of the population's actual distribution.
A confidence interval based on the Central Limit Theorem, there are three key ingredients:
1. A summary statistic (e.g. a mean) from your sample
2. A multiple z, based on a tail area from the normal distribution.
3. A formula for the standard error of your summary statistic.
For a given level of confidence, the z-score corresponds to the number of standard deviations from the mean. The standard error of a summary statistic is a measure of the variability of the estimate that is dependent on the size of the sample, the variability of the population, and the type of summary statistic. The standard error of a sample mean is given by the formula σ/√n, where σ is the population standard deviation and n is the sample size.
Thus, all the above points (1, 2, and 3) are the key ingredients of a confidence interval based on the Central Limit Theorem.
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A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8 ft? Leave your answer in simplest radical form.A. 16B. 2C. 8D. 4
The length of the diagonal is 8√2 ft.
How to find the length of the diagonal if the side of the square is 8 ft?If the side of the square is 8 ft, then the diagonal will form a right triangle with legs of length 8 ft. We can use the Pythagorean theorem to find the length of the diagonal (hypotenuse).
Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
In this case, we have:
a = 8 ft (one leg)
b = 8 ft (the other leg)
c = ? (the hypotenuse)
Using the Pythagorean theorem, we have:
c² = a² + b²
c² = 8² + 8²
c² = 64 + 64
c² = 128
c = √128
c = 8√2 ft
Therefore, the length of the diagonal is 8√2 ft.
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Which expression represents the perimeter of a triangle in simplest form that has side lengths: 2x, 3x + 5, x + 2
Answer:
6x + 7
Step-by-step explanation:
triangle has 3 sides right, which is 2x, 3x+5 and x+2
so basically you just have to add everything up since perimeter is just the total number of each sides combined
2x + (3x+5) + (x+2)
expand from the brackets
2x + 3x + 5 + x + 2
rearrange the numbers to avoid confusion
2x + 3x + x + 5 + 2
add everything up
6x + 7
For both f(x)= √x and f(x)=1/x, sketch the graph of the parent function, apply the transformations indicated, and state the domain and range. Note: You can sketch the graphs by hand or in digital form.
a) y= f(x+2)-1
b) y= -2f(x)+4
c) y= -2f(-(x-3))+1
Answer: a) Parent function:
f(x) = √x
Domain: x ≥ 0
Range: y ≥ 0
Applying transformations:
shift 2 units left: f(x+2)
shift 1 unit down: f(x+2)-1
Final equation and graph:
y = √(x+2) - 1
Domain: x ≥ -2
Range: y ≥ -1
b) Parent function:
f(x) = 1/x
Domain: x ≠ 0
Range: y ≠ 0
Applying transformations:
multiply by -2: -2f(x)
shift 4 units up: -2f(x)+4
Final equation and graph:
y = -2/x + 4
Domain: x ≠ 0
Range: y ≠ 4
c) Parent function:
f(x) = 1/x
Domain: x ≠ 0
Range: y ≠ 0
Applying transformations:
shift 3 units right: f(-(x-3))
multiply by -2: -2f(-(x-3))
shift 1 unit up: -2f(-(x-3))+1
Final equation and graph:
y = -2/(3-x) + 1
Domain: x ≠ 3
Range: y ≠ 1
Step-by-step explanation:
A fair coin is flipped 3 times and a random variable X is defined to be 3 times the number of heads minus 2 times the number of tails. Find the probability mass function of X. (Write it in table format).
The probability mass function of X( -3, -1, 1 ,3) is P(X) 1/8 3/8 3/8 1/8.
A fair coin is flipped 3 times and the random variable X is defined as follows:
X = 3 times the number of heads - 2 times the number of tails
To find the probability mass function of X, we can list all the possible outcomes and calculate their probabilities.
The Possible outcomes are as shown:
3 heads (X = 3)
2 heads, 1 tail (X = 1)
1 head, 2 tails (X = -1)
3 tails (X = -3)
And the Probabilities are:
P(X = 3) = 1/8
P(X = 1) = 3/8
P(X = -1) = 3/8
P(X = -3) = 1/8
Therefore, the probability mass function of X is:
X( -3, -1, 1 ,3) is P(X) 1/8 3/8 3/8 1/8
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In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200 adults are randomly selected for a market research campaign. What is the sampling distribution of their sample mean IQ? Must show work (explain) to justify choice.
- exactly normal, mean 112, standard deviation 20
- approximately normal, mean 112, standard deviation 0.1
- approximately normal, mean 112, standard deviation 1.414
- approximately normal, mean 112, standard deviation 20
The sampling distribution is approximately normal.
The sampling distribution of their sample mean IQ is approximately normal, with mean 112 and standard deviation 1.414.What is the sampling distribution of their sample mean IQ?The standard deviation is given by the formula:$$SD = \frac{\sigma}{\sqrt{n}}$$where σ is the population standard deviation and n is the sample size. So, we have:$${SD} = \frac{20}{\sqrt{200}} = \sqrt{\frac{20^2}{200}} = \sqrt{2} = 1.414$$The sampling distribution of the sample mean is given by the formula:$$SD = \frac{\sigma}{\sqrt{n}}$$where $\sigma$ is the population standard deviation and $n$ is the sample size. Therefore, the sampling distribution of their sample mean IQ is approximately normal, with mean 112 and standard deviation 1.414. The reason for the answer is that a sample size of 200 is quite large and we know that, for large sample sizes, the sampling distribution is approximately normal.
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