Question

Suppose x has a distribution with a mean of 90 and a standard deviation of 36. Random samples of size n = 64 are drawn.

(a) Describe the x-bar distribution and compute the mean and standard deviation of the distribution.

x-bar has _____ (an approximately normal, a binomial, an unknown, a normal, a Poisson, a geometric) distribution with

mean μ_x-bar = _____ and standard deviation σ_x-bar = _____ .

(b) Find the z value corresponding to

x-bar = 99.

z = _____

(c) Find

P(x-bar < 99). (Round your answer to four decimal places.)

P(x-bar < 99) = _____

(d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 99? Explain.

No, it would not be unusual because more than 5% of all such samples have means less than 99.

No, it would not be unusual because less than 5% of all such samples have means less than 99.

Yes, it would be unusual because less than 5% of all such samples have means less than 99.

Yes, it would be unusual because more than 5% of all such samples have means less than 99.

Answer 1

Solution :

Given that ,

mean = = 90

standard deviation = = 36

n = 64

a) is approximately normal

=   = 90

= / n = 36 / 64 = 4.5

b) = 99

Using z-score formula,

z = -   /

z = 99 - 90 / 4.5

z = 2.00

c) P( < 99) = P(( - ) / < (99 - 90) / 4.5)

= P(z < 2.00)

Using z table

= 0.9772

d) No, it would not be unusual because more than 5% of all such samples have means less than 99.