Question

It is suggested that the average IQ of top civil servants, research scientists and professors is 140. Suppose that the standard deviation is 5.
a. Suppose a full professor from a Canadian university is selected at random. What is the probability that the IQ of the selected Canadian professor is below 130? State any necessary assumptions you have made to compute this probability.

b. Suppose that the assumption(s) made in part a was not justifiable. A researcher decided to take a random sample of 81 full professors from the Canadian University system.

i. What is the sampling distribution of the sample mean ¯ x ? Explain.

ii. Find the mean and standard deviation of the sampling distribution of ¯ x.

iii. What is the probability that the sample average of this sample is less than 130? Compare your answer with the answer given in a. Summarize your findings.

iv. Will the probability in (iii) change if you change the wording from “less than” to “less than or equal to”? Why or why not?

v. Can you compute the probability that the sample average IQ is exactly 135? Justify your answer.

vi. If the sample mean ¯ x is actually actually 130, what can be said about the claim that µ = 140.

vii. What is the probability that the sample mean differs from the population mean by more than 2?

viii. Within what limits do you expect the sample average to be with the probability 0.95?

Answer 1

Answer:

a)Here we need to assume that the IQ follows a normal distribution

b)n=81

i)As per central limit theorem, the sampling distribution of is a normal distribution

The value is small because the sample size and large. As per the law of large numbers, if we keep increasing the sample size, the mean of the sample tends to the population mean.

iv)The probability would change if we use a discrete process. But, the current analysis assumes the process is continuous. Hence, the probability would not change

NOTE:: I HOPE YOUR HAPPY WITH MY ANSWER....***PLEASE SUPPORT ME WITH YOUR RATING...

***PLEASE GIVE ME "LIKE"...ITS VERY IMPORTANT FOR ME NOW....PLEASE SUPPORT ME ....THANK YOU

NOTE:: I HOPE YOUR HAPPY WITH MY ANSWER....***PLEASE SUPPORT ME WITH YOUR RATING...

***PLEASE GIVE ME "LIKE"...ITS VERY IMPORTANT FOR ME NOW....PLEASE SUPPORT ME ....THANK YOU