Answered: a) What is the probability that X < 12?…

a) What is the probability that X < 12? b) What is the probability that at least one of the 50 measurements is less than 12? c) What is the expected value of S-(50 * 12.2) ?

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Assume that the fill, X, of a water filling machine is 12.2 with a standard deviation of 0.1 with the measurements being in liquid ounces.
Assume X is a normal random variable. Suppose we independently take 50 such measurements, say X1, X2,
.., X50. Let M be the
sample mean of the 50 measurements. Let S be the sum of the 50 measurements.
a) What is the probability that X < 12?
b) What is the probability that at least one of the 50 measurements is less than 12?
c) What is the expected value of S-(50 * 12.2) ?
d) What is the standard deviation of S- (50 * 12.2) ?
e) What is the probability that S- (50 * 12.2) >1?
f) What is the probability that S- (50 × 12.2) < -0.5?
g) What is the expected value of M?
h) What is the standard deviation of M-12.2?
i) What is the probability that M-12.2>.01?
j) What is the standard deviation of 50*(M-12.2)?
k) What is the variance of 50*(M-12.2)?
I) If the probability of X > k is equal to .05 then what is k.?

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