Question

Suppose x has a distribution with a mean of 40 and a standard deviation of 21. Random samples of size n = 36 are drawn.

(a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has distribution with

mean μx =

and

standard deviation σx = .

(b) Find the z value corresponding to x = 47. z = (c) Find P(x < 47). (Round your answer to four decimal places.)

P(x < 47) =

(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 47? Explain.

No, it would not be unusual because less than 5% of all such samples have means less than 47.

Yes, it would be unusual because more than 5% of all such samples have means less than 47.

Yes, it would be unusual because less than 5% of all such samples have means less than 47.

No, it would not be unusual because more than 5% of all such samples have means less than 47.

Answer 1

Solution :

Given that ,

mean = = 40

standard deviation = = 21

n = 36

a) =   = 40

= / n = 21 / 36 = 3.5

b) = 47

Using z-score formula,

z = -   /

z = 47 - 40 / 3.5

z = 2.00

c) P( < 47) = P(( - ) / < (47 - 40) / 3.5)

= 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 47.