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]

Given, weight of young teen boy normally distributed with mean 97 pound and standard deviation 10.5 pound.a) p(F1>100)=p(F1-μσ>100-μσ) =p(F1-9710.5>100-9710.5) =p(Z>0.2857) =1-p(Z<0.2857) =1-0.612452 .... By using Z table p(F1>100)=0.387548b) Random sample of size =26 is selected from normal distribution, then sum of all normal random variables follows, S~N(∑μ,∑σ2) S~N(∑12697,∑12610.52) S~N(2522,53.542) Hence, Expected value of S is 2522.c) Standard deviation of S is 53.54

Math

Statistics

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? c) What is the standard deviation of S?

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? c) What is the standard deviation of S?

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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