1. Suppose that the data under consideration consists of the heights of the starting fiveplayers on a basketball team:4PlayerHeight (inches) 67 73137576 84a). Compute the mean and the standard deviation for the entire data.b). List all possible samples of size 2 and find the mean of each sample.c). Find the probability distribution of the sample mean. Find the mean and the standarddeviation for this distributiond). Does the Central Limit Theorem apply in this sampling situation? If so, verify it verycarefully.

a) The mean and the standard deviation are mean=sum of the valuestotal number of…

Answered: 1. Suppose that the data under…

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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1. Suppose that the data under consideration consists of the heights of the starting five
players on a basketball team:
4
Player
Height (inches) 67 73
1
3
75
76 84
a). Compute the mean and the standard deviation for the entire data.
b). List all possible samples of size 2 and find the mean of each sample.
c). Find the probability distribution of the sample mean. Find the mean and the standard
deviation for this distribution
d). Does the Central Limit Theorem apply in this sampling situation? If so, verify it very
carefully.

Expert Solution

Step 1: Part a)

a) The mean and the standard deviation are

$\begin{array}{rcl} m e a n & = & \frac{s u m o f t h e v a l u e s}{t o t a l n u m b e r o f v a l u e s} \\ = & \frac{67 + 73 + 75 + 76 + 84}{5} = 75 \\ s \tan d a r d d e v i a t i o n & = & \sqrt{\frac{\sum_{i = 1}^{n} {(x - x)}^{2}}{n - 1}} \\ = & \sqrt{\frac{{(67 - 75)}^{2} + . . . + {(84 - 75)}^{2}}{5 - 1}} \\ = & 6.123724 \end{array}$

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