MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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The average weight of a young teen boy is 97 pounds with a standard deviation of 10.5 pounds. Suppose we randomly select 26 young teen boys and weigh them. The measurements (in pounds) are F1, F2, ..., F26. Let S = F1 + F2 + ... + F26 and let M = S/26. This means S is the sample sum and M is the sample mean of the selected teen boys (Note: random selection means F1 ... F26 are independent.). Assume the Fis are normally distributed.

a) What is the probability that F1 > 100?

b) What is the expected value of S?  
[Box for answer]

c) What is the standard deviation of S?  
[Box for answer]

d) What is the expected value of M?  
[Box for answer]

e) What is the standard deviation of M?  
[Box for answer]

f) What is the expected value of S - 26*97?  
[Box for answer]

g) What is the standard deviation of ZZ =  
\[
\frac{S - 26 \times 97}{\sqrt{26} \times 10.5}
\]  
[Box for answer]

h) What is the probability that ZZ > 2?  
[Box for answer]

i) What is the probability that ZZ < -0.5?  
[Box for answer]

j) What is the variance of 9ZZ?  
[Box for answer]

k) What is the expected value of M - 97?  
[Box for answer]

l) What is the standard deviation of  
\[
\frac{M - 97}{\frac{10.5}{\sqrt{26}}}
\]  
[Box for answer]
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Transcribed Image Text:The average weight of a young teen boy is 97 pounds with a standard deviation of 10.5 pounds. Suppose we randomly select 26 young teen boys and weigh them. The measurements (in pounds) are F1, F2, ..., F26. Let S = F1 + F2 + ... + F26 and let M = S/26. This means S is the sample sum and M is the sample mean of the selected teen boys (Note: random selection means F1 ... F26 are independent.). Assume the Fis are normally distributed. a) What is the probability that F1 > 100? b) What is the expected value of S? [Box for answer] c) What is the standard deviation of S? [Box for answer] d) What is the expected value of M? [Box for answer] e) What is the standard deviation of M? [Box for answer] f) What is the expected value of S - 26*97? [Box for answer] g) What is the standard deviation of ZZ = \[ \frac{S - 26 \times 97}{\sqrt{26} \times 10.5} \] [Box for answer] h) What is the probability that ZZ > 2? [Box for answer] i) What is the probability that ZZ < -0.5? [Box for answer] j) What is the variance of 9ZZ? [Box for answer] k) What is the expected value of M - 97? [Box for answer] l) What is the standard deviation of \[ \frac{M - 97}{\frac{10.5}{\sqrt{26}}} \] [Box for answer]
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