Question

Suppose x has a distribution with a mean of 30 and a standard deviation of 12. Random samples of size

n = 64

are drawn.

(a) Describe the

x distribution

and compute the mean and standard deviation of the distribution.

x

has  ---Select--- an approximately normal a normal a Poisson a geometric a binomial an unknown distribution with

mean μ_x =

and

standard deviation σ_x =  .

(b) Find the z value corresponding to

x = 33.

z =

(c) Find

P(x < 33).

(Round your answer to four decimal places.)

P(x < 33) =

(d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 33? Explain.

No, it would not be unusual because less than 5% of all such samples have means less than 33.Yes, it would be unusual because less than 5% of all such samples have means less than 33.     No, it would not be unusual because more than 5% of all such samples have means less than 33.Yes, it would be unusual because more than 5% of all such samples have means less than 33.

please explain how to put this into a calculator. Thank you!

Answer 1

Solution:- Given that mean = 30, standard deviation 12, n = 64

(a) the x distribution is considered normal

mean μx =30

standard deviation σx = 12/sqrt(64) = 1.5

(b) X = 33

Z = (X-μx)/σx = (33-30)/1.5 = 2

(c) P(X < 33) = P((X-μx)/σx < (33-30)/1.5))
= P(Z < 2)
= 0.9772

(d) Yes, it would be unusual because more than 5% of all such samples have means less than 33.