Question

Suppose x has a distribution with a mean of 80 and a standard deviation of 12. Random samples of size n = 64 are drawn.

(a) Describe the x bar distribution. x bar has an approximately normal distribution. x bar has a Poisson distribution. x bar has a binomial distribution. x bar has an unknown distribution. x bar has a normal distribution. x bar has a geometric distribution. Compute the mean and standard deviation of the distribution. (For each answer, enter a number.) mu sub x bar = mu sub x bar = sigma sub x bar = sigma sub x bar =

(b) Find the z value corresponding to x bar = 83. (Enter an exact number.) z =

(c) Find P(x bar < 83). (Enter a number. Round your answer to four decimal places.) P(x bar < 83) = P(x bar < 83)

(d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 83?

Explain.

Answer 1

Solution :

Given that ,

mean = = 80

standard deviation = = 12

n = 64

a)

x bar has an approximately normal distribution.

= = 80 and

= / n = 12 / 64 = 1.5

b)

= 83

z = ( - ) /

= ( 83 - 80) / 1.5

= 2

c)

P( < 83) = P(( - ) / < (83 - 80) / 1.5)

= P(z < 2)

= 0.9772 Using standard normal table,   

Probability = 0.9772

d)

It be not unusual for a random sample of size 64 from the x distribution to have a sample mean less than 83.

because the probability is greater than 0.05.