Suppose a simple random sample of size nequals64 is obtained from a population with mu equals 88 and sigma equals 8. (a) Describe the sampling distribution of x overbar. (b) What is Upper P (x overbar greater than 89.7 )? (c) What is Upper P (x overbar less than or equals 85.7 )? (d) What is Upper P (87.35 less than x overbar less than 90.5 )?

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 = 64

Part a

Since the sample size is large enough we can use the central limit distribution and the distribution for the sample 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 89.7 we got:

Part c

We can use the z score formula given by:

And if we find the z score for 85.7 we got:

Part d

We want this probability:

We find the z scores:

98%

step-by-step explanation:

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