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

See similar textbooks

Related questions

Concept explainers

Question

The lengths of adult males' hands are normally distributed with a mean of 190 mm and the standard deviation is 7.4 mm. Suppose that 44 individuals are randomly chosen. Round all answers to 4 where possible.

a. What is the distribution of ¯ x ? ¯ x ~ N

b. For the group of 44, find the probability that the average hand length is more than 189.

c. Find the first quartile for the average adult male hand length for this sample size.

Expert Solution

Step 1

Sampling Distribution of a Normal Variable :

Given a random variable X. Suppose that the population distribution of X is known to be normal, with mean µ and
variance σ² , that is, X ~ N(µ, σ). Then, for any sample size n, it follows that the sampling distribution of $\bar{X}$ is normal,
with mean µ and variance σ²/n , that is,

$\bar{X} ~ N (μ, \frac{σ}{\sqrt{n}})$

$\frac{σ}{\sqrt{n}}$ is called the “standard error of the mean,” denoted SEM, or more simply, s.e.

The corresponding Z-score transformation formula is $Z = \frac{\bar{X} - μ}{σ / \sqrt{n}} ~ N (0, 1)$

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions