IQ scores are normally distributed with a mean of100and a standard deviation of15.Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample.a. If the sample size isn=81,find the mean and standard deviation of the distribution of sample means. The mean of the distribution of sample means isnothing.The standard deviation of the distribution of sample means isnothing.(Type an integer or decimal rounded to the nearest tenth as needed.)b. If the sample size isn=169,find the mean and standard deviation of the distribution of sample means. The mean of the distribution of sample means isnothing. The standard deviation of the distribution of sample means isnothing.(Type an integer or decimal rounded to the nearest tenth as needed.)c. Why is the standard deviation in part a different from the standard deviation in part b? Choose the correct answer below. A.With smaller sample sizes (as in part a), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation. B.With larger sample sizes (as in part b), the means tend to be further apart, so they have more variation, which results in a bigger standard deviation. C.With smaller sample sizes (as in part a), the means tend to be further apart, so they have more variation, which results in a smaller standard deviation. D.With larger sample sizes (as in part b), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample.a. If the sample size is n=81, find the mean and standard deviation of the distribution of sample means.The mean of the distribution of sample means is.The standard deviation of the distribution of sample means is(Type an integer or decimal rounded to the nearest tenth as needed)b. If the sample size is n= 169, find the mean and standard deviation of the distribution of sample means.The mean of the distribution of sample means isThe standard deviation of the distribution of sample means is(Type an integer or decimal rounded to the nearest tenth as needed)c. Why is the standard deviation in part a different from the standard deviation in part b? Choose the correct answer below.A. With smaller sample sizes (as in part a), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.B. With larger sample sizes (as in part b), the means tend to be further apart, so they have more variation, which results in a bigger standard deviation.C. With smaller sample sizes (as in part a), the means tend to be further apart, so they have more variation, which results in a smaller standard deviation.O D. With larger sample sizes (as in part b), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.

The following data is given IQ scores are normally distributed with mean 100, and standard deviation…

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Assume that many samples of size n are taken from a large population of people and the mean IQ score is cormputed for each sample a. If the sample size is n=81, find the mean and standard deviation of the distribution of sample means. The mean of the distribution of sample means is The standard deviation of the distribution of sample means is (Type an integer or decimal rounded to the nearest tenth as needed.) b. If the sample size is n= 169 , find the mean and standard deviation of the distribution of sample means. The mean of the distribution of sample means is The standard deviation of the distribution of sample means is (Type an integer or decimal rounded to the nearest tenth as needed) c. Why is the standard deviation in part a different from the standard deviation in part b? Choose the correct answer below. O A. With smaller sample sizes (as in part a), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation. O B. With larger sample sizes (as in part b), the means tend to be further apart, so they have more variation, which results in a bigger standard deviation. O C. With smaller sample sizes (as in part a), the means tend to be further apart, so they have more variation, which results in a smaller standard deviation. O D. With larger sample sizes (as in part b), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

IQ scores are normally distributed with a mean of

100

and a standard deviation of

15.

Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample.

a. If the sample size is

n=81,

find the mean and standard deviation of the distribution of sample means.

The mean of the distribution of sample means is

nothing.

The standard deviation of the distribution of sample means is

nothing.

(Type an integer or decimal rounded to the nearest tenth as needed.)

b. If the sample size is

n=169,

find the mean and standard deviation of the distribution of sample means.

The mean of the distribution of sample means is

nothing.

The standard deviation of the distribution of sample means is

nothing.

(Type an integer or decimal rounded to the nearest tenth as needed.)

c. Why is the standard deviation in part a different from the standard deviation in part b? Choose the correct answer below.

With smaller sample sizes (as in part a), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.

With larger sample sizes (as in part b), the means tend to be further apart, so they have more variation, which results in a bigger standard deviation.

With smaller sample sizes (as in part a), the means tend to be further apart, so they have more variation, which results in a smaller standard deviation.

With larger sample sizes (as in part b), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample.
a. If the sample size is n=81, find the mean and standard deviation of the distribution of sample means.
The mean of the distribution of sample means is.
The standard deviation of the distribution of sample means is
(Type an integer or decimal rounded to the nearest tenth as needed)
b. If the sample size is n= 169, find the mean and standard deviation of the distribution of sample means.
The mean of the distribution of sample means is
The standard deviation of the distribution of sample means is
(Type an integer or decimal rounded to the nearest tenth as needed)
c. Why is the standard deviation in part a different from the standard deviation in part b? Choose the correct answer below.
A. With smaller sample sizes (as in part a), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.
B. With larger sample sizes (as in part b), the means tend to be further apart, so they have more variation, which results in a bigger standard deviation.
C. With smaller sample sizes (as in part a), the means tend to be further apart, so they have more variation, which results in a smaller standard deviation.
O D. With larger sample sizes (as in part b), the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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