For each of the following, answer whether the distribution of X is necessarily normally distributed (YES) or not (NO), and briefly explain why. a) X = the sample mean age for random samples of size n = 50 from the population of New Yorkers of non-working age (defined as below 18 or above 64). b) X = the sample mean age for random samples of size n = 10 from the population of New Yorkers of non-working age (defined as below 18 or above 64). c) X = the sample mean age for random samples of size n = 10 from a population of individuals whose ages are known to be normally distributed.
For each of the following, answer whether the distribution of X is necessarily normally distributed (YES) or not (NO), and briefly explain why. a) X = the sample mean age for random samples of size n = 50 from the population of New Yorkers of non-working age (defined as below 18 or above 64). b) X = the sample mean age for random samples of size n = 10 from the population of New Yorkers of non-working age (defined as below 18 or above 64). c) X = the sample mean age for random samples of size n = 10 from a population of individuals whose ages are known to be normally distributed.
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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Nt 2

Transcribed Image Text:**NT #2**
For each of the following, answer whether the distribution of \( \overline{X} \) is necessarily normally distributed (YES) or not (NO), and briefly explain why.
a) \( \overline{X} \) = the sample mean age for random samples of size \( n = 50 \) from the population of New Yorkers of non-working age (defined as below 18 or above 64).
b) \( \overline{X} \) = the sample mean age for random samples of size \( n = 10 \) from the population of New Yorkers of non-working age (defined as below 18 or above 64).
c) \( \overline{X} \) = the sample mean age for random samples of size \( n = 10 \) from a population of individuals whose ages are known to be normally distributed.
**NT #3**
An unknown distribution has a mean of 40 and a standard deviation of 8. A sample size of 50 is drawn randomly from the population. Find the probability that the sum of the 50 values is greater than 2,400.
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