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:

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation: