Question

Suppose x has a distribution with a mean of 60 and a standard deviation of 21. Random samples of size n = 36 are drawn.

(a) Describe the x bar distribution.

Compute the mean and standard deviation of the distribution. (For each answer, enter a number.)

(b) Find the z value corresponding to x bar = 53.

(c) Find P(x bar < 53). (Enter a number. Round your answer to four decimal places.)

(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 53? Explain.

Answer 1

Solution :

Given that ,

mean = = 60

standard deviation = = 21

n = 36

a) The distribution of is approximately normal.

=   = 60

= / n = 21 / 36 = 3.5

b) = 53

z = -   /

z = 53 - 60 / 3.5

z = -2.00

c) P( < 53) = P(( - ) / < (53 - 60) / 3.5)

= P(z < -2.00)

Using z table

= 0.0228

d) Yes, it would be unusual because less than 5% of all such samples have means less than 53.