In a data set with a normal distribution, the mean is 98 and the standard deviation is 12. About what percent of the data lie between 74 and 122?
Answers
Answer:
B. 95%
Step-by-step explanation:
The mean is in the middle and standard deviation is 12. So subtract 12 from 98 until you get to 74. That's two times. And two times/spaces to the left and right is 95% of the data.
The confidence interval is 95.45% of the data in the data set with a normal distribution
What is Confidence Interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
With a 95 percent confidence interval, you have a 5 percent chance of being wrong. With a 90 percent confidence interval, you have a 10 percent chance of being wrong. A 99 percent confidence interval would be wider than a 95 percent confidence interval
Confidence Interval CI = x + z ( s/√n )
where x = mean
z = confidence level value
s = standard deviation
n = sample size
Given data ,
To find out what percent of the data lie between 74 and 122 in a normal distribution with a mean of 98 and a standard deviation of 12, we can use the empirical rule, also known as the 68-95-99.7 rule, which states that:
Approximately 68% of the data falls within one standard deviation of the mean
Approximately 95% of the data falls within two standard deviations of the mean
Approximately 99.7% of the data falls within three standard deviations of the mean
Based on this rule, we can estimate the percentage of data that lies between 74 and 122 as follows:
Calculate the z-scores for 74 and 122 using the formula: z = (X - mean) / standard deviation
For 74: z = (74 - 98) / 12 = -2
For 122: z = (122 - 98) / 12 = 2
Find the area under the normal curve between these two z-scores using a standard normal distribution table or a statistical calculator.
The area between z = -2 and z = 2 represents the percentage of data that lies between 74 and 122.
Using a standard normal distribution table, we can find that the area between z = -2 and z = 2 is approximately 0.9545 or 95.45%.
Hence , about 95.45% of the data in the data set with a normal distribution would be expected to lie between 74 and 122.
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Related Questions
The first step when multiplying fractions is to find the reciprocal of the second fraction.
O True
O False
Answers
The first step when multiplying fractions is to find the reciprocal of the second fraction.
The statement is False.
The first step when multiplying fractions is to find the reciprocal of the second fraction.
The given statement is FALSE.
Because, First step in multiplying fractions is multiply the numerator from each fraction. That is, multiply the top number first.
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At the store brand a potato chips or $11.90 for four bags
Answers
Answer:
what is the question?
Step-by-step explanation:
i need the question to answer
A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the following table. Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth.
Passed Failed
Male 58 14
Female 98 11
Since P(male)xP(fail) = ___and P(male and fail)= ,___ the two results are_______ - so the events are________
Answers
Answer:
Since P(male)xP(fail) = 0.0549 and and P(male and fail) = 0.0773, the two results are different, so the events are not independent.
Step-by-step explanation:
Independent events:
Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Probability of male:
58 + 14 = 72 males out of 58 + 14 + 98 + 11 = 181
So
P(male) = 72/181 = 0.3978
Probability of failling:
14 + 11 = 25 students fail out of 181. So
P(fail) = 28/181 = 0.1381
Multiplitication of male and failling:
0.3978*0.1381 = 0.0549
Probability of being male and failing:
14 out of 181. So
14/181 = 0.0773
Different probabilities, so not independent.
Since P(male)xP(fail) = 0.0549 and and P(male and fail) = 0.0773, the two results are different, so the events are not independent.
f(n)=n-2
g(n)=4n-1
f{g(n)}=?
Answers
9514 1404 393
Answer:
f(g(n)) = 4n-3
Step-by-step explanation:
f(g(n)) = f(4n -1) = (4n -1) -2
f(g(n)) = 4n -3
Please help will give correct answer brainliest
what information is necessary to prove that the two triangles are similar by the AA similarity theorem? show your work
Answers
Answer:
Step-by-step explanation:
Let us begin with the AA Similarity definition. It states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
This means that we need:
An angle of one triangle that is congruent to an angle of the other triangle.Another angle of one triangle that is congruent to another angle of the other triangle.For this problem, it is unclear that there are more than one angles that are congruent to each other. We see that angle <DEF and <ABC are congruent, but the problem does not give any other angles. In another case, we must find one more to prove similarity by the AA similarity theorem.
For each sequence, state if it is arithmetic, geometric, or neither.
0, 3, 8, 15, 24
Answers
Answer:
Step-by-step explanation:
0, 3, 8, 15, 24, . . .
it is arithmetic
Brady has a card collection with 32 baseball cards, 64 football cards, and 24 baseball cards. He wants to arrange the cards in equal piles, with only one type of card in each pile.
Answers
So you will have 4 piles of baseball cards, 8 piles of football cards, and 3 piles of baseball cards again
(I think you meant basketball cards and if not add 3+4=7 so you get 7 baseball cards if it wasn’t a typo)
Hope this helps :)
Please help I have been stuck this for a while
Answers
Answer:
Option (D)
Step-by-step explanation:
Given expression is,
x³ × 3 ÷ [tex]\frac{2}{9}[/tex] + 9x - (7 - 6x)
By substituting x = [tex]\frac{2}{3}[/tex],
[tex](\frac{2}{3})^3\times 3 \div \frac{2}{9}+9(\frac{2}{3})-[7-6(\frac{2}{3})][/tex]
By using rule PEMDAS,
P - Parenthesis
E - Exponent
M - Multiplication
D - Division
A - Addition
S - Subtraction
[tex]=(\frac{2}{3})^3\times 3 \div \frac{2}{9}+9(\frac{2}{3})-[7-4][/tex]
= [tex](\frac{2}{3})^3\times 3 \div \frac{2}{9}+9(\frac{2}{3})-3[/tex]
= [tex]\frac{8}{27}\times 3 \div \frac{2}{9}+6-3[/tex]
= [tex]\frac{8}{9}\div \frac{2}{9}+6-3[/tex]
= [tex]\frac{8}{9}\times \frac{9}{2}+6-3[/tex]
= 4 + 6 - 3
= 7
Option (D) is the answer.
Write an explicit formula for the An, and the n^th term of the sequence 24,-12,6,....
Answers
Answer:
[tex]T_n = -48* (-\frac{1}{2})^{n}[/tex]
Step-by-step explanation:
Given
[tex]24, -12, 6,...[/tex]
Required
Write a formula
The above sequence shows a geometric sequence because:
[tex]r = \frac{-12}{24} = \frac{6}{-12} = -\frac{1}{2}[/tex] -- common ratio
The equation is determined using:
[tex]T_n = ar^{n-1}[/tex]
Where
[tex]a = 24[/tex]
Substitute values for a and r
[tex]T_n = 24* (-\frac{1}{2})^{n-1}[/tex]
Apply law of indices:
[tex]T_n = 24* (-\frac{1}{2})^{n} * (-\frac{1}{2})^{-1}[/tex]
[tex]T_n = 24* (-\frac{1}{2})^{n} * 1/(-\frac{1}{2})[/tex]
[tex]T_n = 24* (-\frac{1}{2})^{n} * 1*-2[/tex]
[tex]T_n = 1*-2*24* (-\frac{1}{2})^{n}[/tex]
[tex]T_n = -48* (-\frac{1}{2})^{n}[/tex]
The above represents the explicit formula
Which graph represents the parametric equations x = 1 – t2 and y = 2t, where 0 ≤ t ≤ 5?
ANSWER: A
Answers
After plotting the above equation on the coordinate plane, we can see the graph of the function.
What are parametric equations?A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.
We have two parametric equations:
x = 1 – t² and
y = 2t
t = y/2 and
0 ≤ t² ≤ 5
1 ≤ 1 - t²≤ 4
1 ≤ x≤ 4
Plug the above value in x = 1 – t²
x = 1- (y/2)²
x = 1 - y²/4
4x = 4 - y²
y² = 4(1 - x)
Thus, after plotting the above equation on the coordinate plane, we can see the graph of the function.
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Rafael plans to watch 2 movies each month. Write an equation to represent the total number of movies n that he will watch in m months.
Answers
Answer:What is m?
Step-by-step explanation:
Suppose X has an exponential distribution with mean equal to 11. Determine the following: (a) (Round your answer to 3 decimal places.) (b) (Round your answer to 3 decimal places.) (c) (Round your answer to 3 decimal places.) (d) Find the value of x such that . (Round your answer to 2 decimal places.)
Answers
Answer:
[tex]P(X > 11) = 0.368[/tex]
[tex]P(X > 22) = 0.135[/tex]
[tex]P(X > 33) = 0.050[/tex]
[tex]x = 33[/tex]
Step-by-step explanation:
Given
[tex]E(x) = 11[/tex] --- Mean
Required (Missing from the question)
[tex](a)\ P(X>11)[/tex]
[tex](b)\ P(X>22)[/tex]
[tex](c)\ P(X>33)[/tex]
(d) x such that [tex]P(X <x)=0.95[/tex]
In an exponential distribution:
[tex]f(x) = \lambda e^{-\lambda x}, x \ge 0[/tex] --- the pdf
[tex]F(x) = 1 - e^{-\lambda x}, x \ge 0[/tex] --- the cdf
[tex]P(X > x) = 1 - F(x)[/tex]
In the above equations:
[tex]\lambda = \frac{1}{E(x)}[/tex]
Substitute 11 for E(x)
[tex]\lambda = \frac{1}{11}[/tex]
Now, we solve (a) to (d) as follows:
Solving (a): P(X>11)
[tex]P(X > 11) = 1 - F(11)[/tex]
Substitute 11 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-\frac{1}{11}* 11})[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-\frac{11}{11}})[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-1})[/tex]
Remove bracket
[tex]P(X > 11) = 1 - 1 + e^{-1}[/tex]
[tex]P(X > 11) = e^{-1}[/tex]
[tex]P(X > 11) = 0.368[/tex]
Solving (b): P(X>22)
[tex]P(X > 22) = 1 - F(22)[/tex]
Substitute 22 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-\frac{1}{11}* 22})[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-\frac{22}{11}})[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-2})[/tex]
Remove bracket
[tex]P(X > 22) = 1 - 1 + e^{-2}[/tex]
[tex]P(X > 22) = e^{-2}[/tex]
[tex]P(X > 22) = 0.135[/tex]
Solving (c): P(X>33)
[tex]P(X > 33) = 1 - F(33)[/tex]
Substitute 33 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-\frac{1}{11}* 33})[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-\frac{33}{11}})[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-3})[/tex]
Remove bracket
[tex]P(X > 33) = 1 - 1 + e^{-3}[/tex]
[tex]P(X > 33) = e^{-3}[/tex]
[tex]P(X > 33) = 0.050[/tex]
Solving (d): x when [tex]P(X <x)=0.95[/tex]
Here, we make use of:
[tex]P(X<x) = F(x)[/tex]
Substitute [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X<x) = 1 - e^{-\lambda x}[/tex]
So, we have:
[tex]0.95 = 1 - e^{-\lambda x}[/tex]
Subtract 1 from both sides
[tex]0.95 -1= 1-1 - e^{-\lambda x}[/tex]
[tex]-0.05=- e^{-\lambda x}[/tex]
Reorder the equation
[tex]e^{-\lambda x} = 0.05[/tex]
Substitute 1/11 for [tex]\lambda[/tex]
[tex]e^{-\frac{1}{11} x} = 0.05[/tex]
Solve for x:
[tex]x = -\frac{1}{1/11}\ ln(0.05)[/tex]
[tex]x = -11\ ln(0.05)[/tex]
[tex]x = 32.9530550091[/tex]
[tex]x = 33[/tex] --- approximated
12. x + y = 4
And the next question is
13. -7 x = y
Pls answer ASAP and explain why!! Thank you!!
Answers
Answer:
[tex]x = - \frac{2}{3} \: \: \: y = \frac{14}{3} [/tex]
Step-by-step explanation:
Since we know -7x=y we use the substitution method and plug it in the top equation.
[tex]x + - 7x = 4[/tex]
[tex] - 6x = 4[/tex]
[tex]x = - \frac{4}{6} [/tex]
or x=-2/3
Then plug it back in the the bottom equation
[tex] - 7( \frac { - 2}{3} ) = y[/tex]
y=14/3
Which expression is equivalent to -2 (x +7) - 6x
A. -8x + 14
B. 4x + 14
C. 8x - 7
D. -8x - 7
Answers
Please help with this question ASAP
Answers
Answer:
B. 28/15
Step-by-step explanation:
7/3 x 4/5 = 28/15
Can anyone help explain this my daughter is 7 does not understand it
Answers
i got 413 pointssssssssssssssssssssss who wants em cuz i am leaving brainlry for answers
Answers
Answer:
ayooo i'll take it
Step-by-step explanation:
thanks
Answer:
Ooh a couple more for 100 points!!
Step-by-step explanation:
MATRIX X IS SHOWN BELOW
Answers
Answer:
4
Step-by-step explanation: thast it
Answer: 40
Step-by-step explanation:
Please help me now!!!!
Answers
Answer:
20
Step-by-step explanation:
Answer:
Hello! I hope you are having a great day~
Here is the answer:
Mean Absolute Deviation (MAD): 4.33
Step-by-step explanation:
Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set. So the average distance is 4.33! It has already been rounded to the hundredth place
Mark is thinking of a square number whose digits add up to seven.
Write down two numbers he could be thinking of
Answers
Answer:
16 and 25
Step-by-step explanation:
list perfect square numbers from 1 to 10
1, 4,9,16,25,36,49,64,81,100
looking at the list, 2 numbers he could be thinking of are 16 and 25
360,000 = X% of 4000000
Answers
360,000 / 4000000=.09
.09x100= 9%
Answer:
09
Step-by-step explanation:
1
1 point
The force, I needed to move a rock varies inversely as the length, L, of the crowbar used. When the length is 80 cm, the force needed is 1.5 N. Find the force needed when
the length of the crowbar is 120 cm
Type your answer..
3
Answers
9514 1404 393
Answer:
1.0 N
Step-by-step explanation:
When the length increases by the factor 120/80 = 3/2, the force required is multiplied by the inverse of this: 2/3.
The required force is ...
(2/3)(1.5 N) = 1.0 N
A triangle is dilated by scale factor of 1/5 in a rotated night degrees clockwise about the origin why is the image similar to the pre image
Answers
9514 1404 393
Answer:
conditions for similarity are not violated by the transformation
Step-by-step explanation:
Dilation changes linear measures proportionally, and has no effect on angles. Rotation changes neither lengths nor angles. Hence the dilated, rotated triangle has the same angles as the original, and has proportional side lengths. Those are the requirements for figures to be similar, so the triangles are similar.
Answer:
The corresponding angles of the triangles are congruent
The image is a reduction of the pre-image
Neither the dilation nor the rotation change the shape of the triangle
Explanation:
For shapes to be similar:
1- there should be a ratio between the sides
2- angles in first shape should be congruent to angles in second shape
Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes
Let's check the choices:
1- The corresponding sides of the triangles are congruent:
This option is incorrect as dilation changes the lengths of the sides
2- The corresponding angles of the triangles are congruent:
This option is correct as neither dilation nor rotation alters the measures of the angles
3- The corresponding sides of the image are 5 times as long as those of the pre-image:
This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image
4- The image is a reduction of the pre-image:
This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced
5- Neither the dilation nor the rotation change the shape of the triangle:
This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths)
6- The rotation reduces the size of the triangle:
This option is incorrect as rotation does not alter the size of the shape. It only changes its position
Hope this helps :)
The equation p = 100 – 5t represents the percent p of battery power remaining in a tablet after t hours.
Answers
Answer:
t=-p/5+20
Step-by-step explanation:
p=100−5t
Swap sides so that all variable terms are on the left hand side.
100−5t=p
Subtract 100 from both sides.
−5t=p−100
Divide both sides by −5.
−5t/5 = p - 100/-5
Dividing by −5 undoes the multiplication by −5.
t = p - 100/-5
Divide p−100 by −5.
t=-p/5+20
What is the area of a circle with a diameter of 34 mi? Use 3.14 for n
O 213.52 mi2
0907.46 mi2
O 106.76 mi2
0 3629.84 mi2
Answers
Answer:
907.46
Step-by-step explanation:
diameter = 34
radius = 17 (half of diameter)
A=πr^2
HOPE THIS HELPS PLZ MARK BRAINLIEST! :)
what is the value of z in the equation 4 x 2- z=7?
Answers
Hope this helped! :)
Answer:
Z = 1
Step-by-step explanation:
Simplify the equation using PEMDAS.
4 x 2 - z = 7
8 - x = 7
- x = 7 - 8
-x = - 1
x = 1
Write and solve a proportion to answer the question. 30% of what number is 9?
Answers
Answer:
The answer would be 30.
Step-by-step explanation:
Calculating 9×100÷30 equals 30 and that would be your answer.
Answer:
30
Step-by-step explanation:
30% * x = 9
x = 9/30%
x = 9/0.3
x = 30.
So, 30 is the number
401(<) the contributions are tax deductible, and income generated by the account is
401(k), the contributions are taxable when deposited, but when the money is withdrawn at retirerment they are
In a traditional
In a Roth
Answers
Answer:
First Blank: Traditional
Second Blank: (the other choice, besides exempt)
Third Blank: Roth
Fourth Blank: Taxes exempt
Step-by-step explanation:
I got 5/5 on the test by reading through the other guys answer.
In a traditional 401(k), it is tax deferred because the income earned isn't taxed until the money is withdrawn.
What is income tax?Income tax is a tax applied on individuals or entities concerning income or profit earned by them.
A 401 k is a qualified tax-advantaged saving retirement plan. Usually, The 401K plans are employer-sponsored. Employee contributions to the 401 k plans are deducted from the payroll before the taxes can be calculated.
This means that the employee contribution is not taxed at the time it's withheld by the employer.
The amounts saved are invested in market securities such as shares and companies bonds. The tax due from the money from the investment is deferred to the time of withdrawal.
The employee are needed to pay taxes on contributions and investments earning every financial year.
In a traditional 401(k), it is tax deferred because the income earned isn't taxed until the money is withdrawn.
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Which set of ordered pairs represents a function?
{(-7,-1), (7,-1),(-9,3), (-9,2)}
{(3,5), (7,9),(4,4), (3,3)}
{(3,-2), (-7,6),(-5, -8), (3, -6)}
{(0,2).(-9,7),(-6, -1),(-2,2)}
Answers
Answer:
The last one
Step-by-step explanation:
Answer:
{(0,2), (-9,7), (-6, -1), (-2,2)}
Step-by-step explanation:
You can see if points are a function by seeing if the first value in the parenthesis (X value) and if they are the same, the points are not a function. The only points where the first value in the parenthesis are not the same is in the fourth set of points.
find the measure of the missing angle to the nearest degree, with showing your work.
Answers
[tex]\cos\theta=\frac{10}{14}\\ \\
\theta=\cos^{-1}\frac{10}{14}\\ \\
\theta=44^o [/tex]