The lengths of adult males' hands are normally distributed with mean 185 mm and standard deviation is 7.5 mm. Suppose that 18 individuals are randomly chosen. Round all answers to 4 where possible.What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)For the group of 18, find the probability that the average hand length is less than 186. Find the third quartile for the average adult male hand length for this sample size. For part b), is the assumption that the distribution is normal necessary? NoYes

Answered: The lengths of adult males' hands are…

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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The lengths of adult males' hands are normally distributed with mean 185 mm and standard deviation is 7.5 mm. Suppose that 18 individuals are randomly chosen. Round all answers to 4 where possible.

What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For the group of 18, find the probability that the average hand length is less than 186.
Find the third quartile for the average adult male hand length for this sample size.
For part b), is the assumption that the distribution is normal necessary? NoYes

Expert Solution

Step 1

Given ,

The lengths of adult males' hands are normally distributed.

Mean = $μ$ = 185 mm

Standard deviation = $σ$ = 7.5 mm

Sample size = n = 18

Sampling distribution of sample mean ( $\bar{x}$ ) :-

If simple random sample of size n is drawn from Normal population with mean $μ$ and standard deviation $σ$ then sampling distribution of sample mean $\bar{x}$ is approximately normal with mean $μ_{\bar{x}} = μ$ and standard deviation $σ_{\bar{x}} = \frac{σ}{\sqrt{n}}$

So, mean of $\bar{x} = μ_{\bar{x}} = μ = 185$

Standard deviation of $\bar{x} = σ_{\bar{x}} = \frac{σ}{\sqrt{n}} = \frac{7.5}{\sqrt{18}} = 1.7678$

Therefore, the distribution of is , $x ~ N (185, 1.7678)$

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