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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

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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