A simple random sample of size nequals81 is obtained from a population with mu equals 83 and sigma equals 27. (a) Describe the sampling distribution of x overbar. (b) What is Upper P (x overbar greater than 89 )? (c) What is Upper P (x overbar less than or equals 75.65 )? (d) What is Upper P (79.4 less than x overbar less than 89.3 )?

a)

With:

b)

c)

d)

Step-by-step explanation:

For this case we know the following propoertis for the random variable X

We select a sample size of n = 81

Part a

Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

With:

Part b

We want this probability:

We can use the z score formula given by:

And if we find the z score for 89 we got:

Part c

We can use the z score formula given by:

And if we find the z score for 75.65 we got:

Part d

We want this probability:

We find the z scores:

yes

step-by-step explanation:

yes