Answer is in the file below
tinyurl.com/wpazsebu
2.
Select the correct answer.
The national apple growers organization recently released its first crop of a new apple variety. It gathered data on the weight of the new apples.
It found a population mean of 4.85 ounces and a standard deviation of 0.92. Each sample size was 500 apples. By the central limit theorem,
which interval do 99.7% of the sample means fall within?
OA.
4.81 and 4.89
OB.
4.73 and 4.97
Ос. .
4.84 and 4.86
OD
4.77 and 4.93
Answer:
B. 4.73 and 4.97
Step-by-step explanation:
To solve this question, we need to understand the Empirical Rule and the Central Limit Theorem.
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard deviation of 0.92, sample of 500:
This means that [tex]\sigma = 0.92, n = 500, s = \frac{0.92}{\sqrt{500}} = 0.04[/tex]
By the central limit theorem, which interval do 99.7% of the sample means fall within?
Within 3 standard deviations of the mean. So
4.85 - 3*0.04 = 4.85 - 0.12 = 4.73
4.85 + 3*0.04 = 4.85 + 0.12 = 4.97
So, option B.
Answer:
4.73 and 4.97
Please give me brainliest, I really need it.
Consider the proposition
2x + 5 > 13
(a) is the condition x > 0 necessary, or sufficient, or both necessary and sufficient for the
inequality to be satisfied?
(b) Answer the same question when x 0x is replaced by x 50
(c) Answer the same question when x > 0 is replaced by x > 4.
your answer is C
your answer is C
your answer is C
your answer is C
your answer is C
Answer:
C
Step-by-step explanation:
2x+5=13
2x+5-5=13-5
2x=8
2x/2=8/2
X=4
if the circumference of a circle is 52 cm, what is the radius? round to the nearest tenth. PLESE HELP I DONT HAVE THAT MUCH TIME :(
Answer:
8.3
Step-by-step explanation:
Given,
Circumference of the circle = 52 cm
Therefore ,
By the problem,
[tex] = > 2\pi r = 52[/tex]
[tex] = > 2 \times 3.14 \times r = 52[/tex]
[tex] = > r = \frac{52}{3.14 \times 2} [/tex]
=> r = 8.2802547771
Rounded to nearest tenth,
=> r = 8.3 (Ans)
HELP ME PLEASEE !! ILL MARK BRAINLIST
Answer:
A) 35
Step-by-step explanation:
x + 50 + 95 = 180
x + 145 = 180
x = 180 - 145
x = 35
please answer!!!! will give brainliest
Answer:
8
Step-by-step explanation:
Hello There!
The median is the middle number of the set
So the first thing we want to do is put the numbers in order from greatest to least
0, 3, 4, 8, 10, 15, 20
Then we go to the middle number
The middle number is 8 so the answer is 8
Answer:
Im pretty sure its 10
The radius of a circle is 3 centimeters. What is the circle's circumference?
=3 cm
Use 3.14 for a.
centimeters
Step-by-step explanation:
The formula for a circumference of a circle is 3.14×diameter
3.14 × (3×2)
3.14×6
18.85
4. Complete the table below that shows the distance Bryan's family has tseveles
to their summer house. The house is 600 miles wizy. After 30 minutes, they are
562.5 miles left to their destination.
Time
Miles
30 minutes
240 minutes
480 minutes
600
1815
5. Jasmine mails 2 CDs in an envelope and the envelope weighs 6 ounces. W
an algebraic expression and calculate the weight of 240 CDs.
Answer:
4-
30 minutes --- 562.5 miles
240 minutes --- 300 miles
480 minutes --- 0 miles
600 minutes --- 150 negative miles (they would have already arrived).
5- 240 CDs will weigh 720 ounces.
Step-by-step explanation:
4- Given that Bryan family's summer house is 600 miles away, and after 30 minutes, they are 562.5 miles left to their destination, to determine the distance in the following minutes the following calculations must be performed:
30 minutes --- 562.5 miles
240 minutes --- 300 miles
600 - 562.5 = (37.5) / 30 = (1.25) x 240 = 300 miles
480 minutes --- 0 miles
600 - 562.5 = (37.5) / 30 = (1.25) x 480 = 600 miles
600 minutes --- 150 negative miles
600 - 562.5 = (37.5) / 30 = (1.25) x 600 = 750 miles
5- Given that Jasmine mails 2 CDs in an envelope and the envelope weighs 6 ounces, to calculate the weight of 240 CDs the following algebraic calculation must be performed:
6/2 x 240 = X
3 x 240 = X
720 = X
Thus, 240 CDs will weigh 720 ounces.
An ice cream shop sells two type of cones: cake cones for $1.75 and waffle cones for $3.25. on tuesday, they sold 50 more waffles cones than cake cones. The total money they collected on cone sales on tuesday was $1422.50. How many cake cone did they sell on tuesday?( this is a matrix word problem)
Answer:
sorry no idea
Step-by-step explanation:
Answer:
252 Cake Cones
Step-by-step explanation:
You have to make your own formula with the numbers in the problem. Here's how I set it up:
w= number of waffle cones
c=number of cake cones
We know that the number of waffle cones is the number of cake cones plus 50, so we write that out here: w=c+50
And we know that the sales total was $1422.50. That is, the number of waffle cones times the cost per cone plus the number of cake cone times their cost per cone, and we can write that out here: (3.25× w) + (1.75×c) =1,422.50.
Now, we can substitute our first formula into the second formula to solve for C. The new equation reads: 3.25(c+50) + 1.75c=1,422.50
Distribute 3.25 to c and 50: 3.25c +162.50+1.75c=1,422.50
Combine like terms: 5c +162.50=1422.50
Subtract 162.50 from both sides: 5c=1260
Divide both sides by 5: C=252
TO CHECK YOUR WORK
Now that you have solved for C, plug that figure back into the first equation to solve for w: (252)+50=w, W=302
Now plug both numbers into your equation for the total cost:
3.25(302) + 1.75(252)=1,422.50
981.5+441= 1,422.50
You're done!
Within a computer program, the number of bugs (i.e., coding errors) per lines of code has a Poisson distribution with an average of fifteen bugs per 1,000 lines. a. Find the probability that there will be exactly eight bugs in 1,000 lines of code. b. Find the probability that there will be at least eight bugs in 1,000 lines of code. c. Find the probability that there will be at least one bug in 1,000 lines of code. d. Find the probability that there will be no more than
Answer:
[tex]P(X=8) = 0.0194[/tex]
[tex]P(X \ge 8)= 0.9820[/tex]
[tex]P(X \ge 1)= 1[/tex]
[tex]P(X\le 1) = 0.0000049[/tex]
Step-by-step explanation:
Given
[tex]\lambda = 15[/tex]
Poisson distribution is given by:
[tex]P(X=x) = \frac{\lambda^x e^{-\lambda}}{x!}[/tex]
Solving (a): 8 bugs
This implies that:
[tex]x = 8[/tex]
So, we have:
[tex]P(X=8) = \frac{15^8 * e^{-15}}{8!}[/tex]
[tex]P(X=8) = \frac{783.99418938}{40320}[/tex]
[tex]P(X=8) = 0.0194[/tex]
Solving (b): At least 8 bugs
This is represented as: [tex]P(X \ge 8)[/tex]
Using complement rule:
[tex]P(X \ge 8)= 1 - P(X<8)[/tex]
Where
[tex]P(X<8) = P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7)[/tex]
[tex]P(X<8) = \frac{15^1 * e^{-15}}{1!} + \frac{15^2 * e^{-15}}{2!} + \frac{15^3 * e^{-15}}{3!} + \frac{15^4 * e^{-15}}{4!} + \frac{15^5 * e^{-15}}{5!} + \frac{15^6 * e^{-15}}{6!} + \frac{15^7 * e^{-15}}{7!}[/tex]
[tex]P(X<8) = (\frac{15^1}{1!} + \frac{15^2}{2!} + \frac{15^3 }{3!} + \frac{15^4}{4!} + \frac{15^5}{5!} + \frac{15^6}{6!} + \frac{15^7}{7!}) e^{-15}[/tex]
[tex]P(X<8) = (15 + 112.5 + 562.5 + 2109.375 + 6328.125 + 15820.3125 + 33900.6696429) *e^{-15}[/tex]
[tex]P(X<8) = 58848.4821429 *e^{-15}[/tex]
[tex]P(X<8) = 0.0180[/tex]
So:
[tex]P(X \ge 8)= 1 - P(X<8)[/tex]
[tex]P(X \ge 8)= 1 - 0.0180[/tex]
[tex]P(X \ge 8)= 0.9820[/tex]
Solving (c): At least 1
This is represented as: [tex]P(X \ge 1)[/tex]
Using complement rule:
[tex]P(X \ge 1)= 1 - P(X<1)[/tex]
[tex]P(X<1) = P(X = 0)[/tex]
[tex]P(X<1) = \frac{15^0 e^{-15}}{0!}[/tex]
[tex]P(X<1) = \frac{e^{-15}}{1}[/tex]
[tex]P(X<1) = e^{-15}[/tex]
So:
[tex]P(X \ge 1)= 1 - P(X<1)[/tex]
[tex]P(X \ge 1)= 1 - e^{-15[/tex]
[tex]P(X \ge 1)= 0.99999969409[/tex]
[tex]P(X \ge 1)= 1[/tex]
Solving (d): Not more than 1
This implies at most 1.
It is represented as:
[tex]P(X\le 1)[/tex]
It is calculated using:
[tex]P(X\le 1) = P(X = 0) + P(X =1)[/tex]
[tex]P(X = 0) = e^{-15}[/tex]
[tex]P(X=1) = \frac{15^1 * e^{-15}}{1!}[/tex]
[tex]P(X=1) = 15 * e^{-15}[/tex]
So:
[tex]P(X\le 1) = e^{-15} + 15 * e^{-15}[/tex]
[tex]P(X\le 1) = 0.00000489443[/tex]
[tex]P(X\le 1) = 0.0000049[/tex]
leah went to a store she baought 5 bags of can food and 5 tore more the next day
What is the question exactly? Ill answer when you tell me
Answer:
Hi how are you doing today Jasmine
The measure of an angle is 42.89. What is the measure of its supplementary angle?
Answer:
The supplementary angle is 137.11.
Step-by-step explanation:
180-42.89 = 137.11
Hope this helps!
Which equation is true for the value x = 15?
Answer:
2x-15=15
where x=15
2(15)-15=15
30-15=15
Answer:
2x-15=15
where x=15
2(15)-15=15
30-15=15
which multiplication equation describes the picture of the third pies below?
Answer:4x1/3=4/3
Step-by-step explanation:
In the pictures there’s 4 one thirds and if u add them together is 4/3
(x+6)/(x+1)=6/2
Solving proportions
Answer:
[tex]x = \frac{3}{2} [/tex]
Step-by-step explanation:
[tex] \frac{x + 6}{x + 1} = \frac{6}{2} [/tex]
[tex] \frac{6}{2} = 3[/tex]
so, the solution of the equation will be as follows:
[tex] \frac{x + 6}{x + 1} = 3[/tex]
3(x+1) = x + 6
3x + 3 = x + 6
3x - x = 6 - 3
[tex]x = \frac{3}{2} [/tex]
so, the answer will be x = 3/2
if you can answer correctly I will cash app you my cash app is cathackley
Answer:
yo i know the answer its 5$ for me to help
Step-by-step explanation:
please help with this math question! and explain to me please so i understand
Answer:
360 - 98 = 262
Step-by-step explanation:
The admission fee at a local zoo is $1.50 for children and $4.00 for adults. On a certain day, 1,900 people enter the zoo and $5,600.00 is collected.
I dont understand the first 4
Answer:
Let me see what i can do, I'll try. Hope this helps
find the value of 0.7 +15.352+2
Answer:
wouldn't this be 18.052
Step-by-step explanation:
add 15 and 2 then add 1 (from 0.7 plus 0.3) then add the other decimals
Answer: 18.052
Step-by-step explanation:
We just need to add them all.
15.352+0.7=16.052 16.052+2=18.052
9 Henry has a length of string that is 2,850 centimeters
long. He needs some pieces that are 78 centimeters
long for an art project. What is the greatest number
of pieces that Henry can cut?
What is a explanation
Answer:
36
Step-by-step explanation:
2850/78 = 36.538
Answer:
36.538
Step-by-step explanation:
since he has 2,850 worth of string and he needs 78 pieces, you would divide 2,850 by 78 which gives you 36.53846154 but you would make it 36.538. if you needed to round by the tenths, its 36.5, hundredths is 36.54, and thousandths is 36.538.
find an ordered pair (x, y) that is a solution to the equation 4x-y=5
Answer:
An ordered pair that is a solution to the equation is (2,3).
Step-by-step explanation:
To find an ordered pair that is a solution to the equation, we attribute a value to one of the variables(x or y), and find the other.
4x-y=5
Using y = 3
4x - 3 = 5
4x = 8
x = 8/4 = 2
An ordered pair that is a solution to the equation is (2,3).
PLEASE HELP, IF ITS RIGHT ILL GIVE U BRAINLIEST THINGY
Answer:
The answer is 8
Step-by-step explanation:
Explicit formula for
1,5,3,6,12
Write the fraction as a decimal 1/2
Answer:
The answer is 0.5
Which point shows a reflection of point X(9, -2) over the x-axis?
Please help me with this question!!
P.S you need to sort it
Answer:
what grade are u?
Step-by-step explanation:
I'm assuming you want to know what "x"is. If so then for the first one x is 1/7. For the second one x= 5. And the last one is x= 3.
Step-by-step explanation:
To check you just substitute what ever x equals into the equation so 35x+5=10 would be 35(1/7)+5=10 and it should equal 10=10, which means infinite solutions. If you were not trying to find out what x equals then what are you looking for exactly?
which situation shows a constant rate of change?
Answer: option D
Step-by-step explanation: just did it
C was wrong and showed option D was the correct answer
Pleas help I will give brainliest also please show how you did it please
Answer:
for n ≤ 3
we are going to put a circle on the 3 and make it filled in then you are going to start an arrow starting from the 3 going to the left all the way to the -10.
Answer:
n ≥ -1 or n ≤ 3
Combined:
-1 ≤ n ≤ 3
Since the inequalities are ≤, it'll be a closed circle
The closed circle will start AT -1 and another closed circle will end at 3
Christa and James both walk from their houses to the bus stop every morning. Christa walks 1.9 kilometers further, and together they walk 4.1 kilometers.
If James walks a distance of d kilometers find the value of d.
Answer:
James walks 2.2 kilometers it is because 4.1-1.9=2.2
Step-by-step explanation:
and to check u can add 2.2 in 1.9 ko get 4.1 so james walked 2.2 distance kilometers from his house.
Answer:
Step-by-step explanation:
d + (d+1.9) = 4.1
2d = 2.2
d = 1.1 km
Suppose that in the production of 60-ohm radio resistors, nondefective items are those that have a resistance between 58 and 62 ohms and the probability of a resistor’s being defective is The resistors are sold in lots of 200, with the guarantee that all resistors are nondefective. What is the probability that a given lot will violate this guarantee? (Use the Poisson distribution.)
Answer:
The probability that a given lot will violate this guarantee is [tex]1 - e^{-200x}[/tex], in which x is the probability of a resistor being defective.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
The probability of a resistor’s being defective is x:
This means that [tex]\mu = nx[/tex], in which n is the number of resistors.
The resistors are sold in lots of 200
This means that [tex]n = 200[/tex], so [tex]\mu = 200x[/tex]
What is the probability that a given lot will violate this guarantee?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = 0) = \frac{e^{-200x}*(200x)^{0}}{(0)!} = e^{-200x}[/tex]
So
[tex]P(X \geq 1) = 1 - e^{-200x}[/tex]
The probability that a given lot will violate this guarantee is [tex]1 - e^{-200x}[/tex], in which x is the probability of a resistor being defective.