I need some help with this question as it requires to round decimal answers to at least 3 places. It is for sections h.), j.), and k.). Assume that the score, X, on the final of MAT 301 is a normally distributed random variable with a mean of 63 and a standard deviation of 10. Suppose that we simulate 180 such measurements, say X1, X2, ..., X180. Let M be the sample mean of the 180measurements. Let S be the sum of the 180 measurements.a) What is the probability that X < 50? 0.0968b) What is the probability that at least one of the 180 measurements is greater than 90? 0.468c) What is the expected value of S? 11340d) What is the standard deviation of S? 134.16e) What is the probability that S- 180*63 >51? 0.352f) What is the probability that S- 180.63 < -58? 0.3336g) What is the expected value of M? 63h) What is the standard deviation of M - 63?i) What is the probability that M-63>0.51? 0.2483j) What is the standard deviation of 180*(M-63)?Enter a number.k) What is the variance of 180*(M-63)?I) If the probability of X > k is equal to .2 then what is k? 71.4

Answered: Image /qna-images/answer/0c82a75a-fa1d-4220-a83c-0e600bd0291d.jpg

h) What is the standard deviation of M - 63? i) What is the probability that M-63>0.51? 0.2483 ) What is the standard deviation of 180"(M-63)| Enter a number. k) What is the variance of 180*(M-63)? I) If the probability of X > k is equal to .2 then what is k? 71.4

h) What is the standard deviation of M - 63? i) What is the probability that M-63>0.51? 0.2483 ) What is the standard deviation of 180"(M-63)| Enter a number. k) What is the variance of 180*(M-63)? I) If the probability of X > k is equal to .2 then what is k? 71.4

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

I need some help with this question as it requires to round decimal answers to at least 3 places. It is for sections h.), j.), and k.).

Assume that the score, X, on the final of MAT 301 is a normally distributed random variable with a mean of 63 and a standard deviation of 10. Suppose that we simulate 180 such measurements, say X1, X2, ..., X180. Let M be the sample mean of the 180
measurements. Let S be the sum of the 180 measurements.
a) What is the probability that X < 50? 0.0968
b) What is the probability that at least one of the 180 measurements is greater than 90? 0.468
c) What is the expected value of S? 11340
d) What is the standard deviation of S? 134.16
e) What is the probability that S- 180*63 >51? 0.352
f) What is the probability that S- 180.63 < -58? 0.3336
g) What is the expected value of M? 63
h) What is the standard deviation of M - 63?
i) What is the probability that M-63>0.51? 0.2483
j) What is the standard deviation of 180*(M-63)?
Enter a number.
k) What is the variance of 180*(M-63)?
I) If the probability of X > k is equal to .2 then what is k? 71.4

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