Answered: Provided are the mean and standard…

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

Provided are the mean and standard deviation among samples of DI Safeties (S), Linebackers (LB), Edge Rushers (EDGE), Defensive Ends (DE), and Defensive Tackles (DT).

1) Consider 25 bunch presses ”elite” and calculate the probability for each defensive position of having ”elite strength”. Which position has the most ”elite strength”?

Bench Presses	DE	DT	Edge	LB	S
Mean	23.0	28.1	22.8	20.0	16.4
Std Dev	3.4	4.5	3.8	4.3	3.5

Expert Solution

Step 1

Here, we have to calculate P(X>25) for each defensive position.

Using standard normal table, we can find these probabilities as follows:

For Defensive Ends (DE):

$P (X > 25) = P (\frac{X - μ}{σ} > \frac{25 - 23.0}{3.4}) = P (z > 0.588) = 1 - P (z < 0.588) = 1 - 0.7217 = 0.2783$

For Defensive Tackles (DT):

$P (X > 25) = P (\frac{X - μ}{σ} > \frac{25 - 28.1}{4.5}) = P (z > - 0.689) = P (z < 0.689) = 0.7546$

For Edge Rushers (EDGE)

$P (X > 25) = P (\frac{X - μ}{σ} > \frac{25 - 22.8}{3.8}) = P (z > 0.579) = 1 - P (z < 0.579) = 1 - 0.7187 = 0.2813$

Step 2

For Linebackers (LB):

$P (X > 25) = P (\frac{X - μ}{σ} > \frac{25 - 20.0}{4.3}) = P (z > 1.163) = 1 - P (z < 1.163) = 1 - 0.8776 = 0.1224$

For DI Safeties (S):

$P (X > 25) = P (\frac{X - μ}{σ} > \frac{25 - 16.4}{3.5}) = P (z > 2.457) = 1 - P (z < 2.457) = 1 - 0.993 = 0.007$

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