Question

Suppose x has a distribution with a mean of 90 and a standard deviation of 3. 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  ---Select--- a normal a geometric an unknown a Poisson a binomial an approximately normal distribution with

mean μ_x =

and

standard deviation σ_x =  .

(b) Find the z value corresponding to

x = 91.

z =

(c) Find

P(x < 91).

(Round your answer to four decimal places.)

P(x < 91) =

(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 91? Explain.

No, it would not be unusual because less than 5% of all such samples have means less than 91.No, it would not be unusual because more than 5% of all such samples have means less than 91.     Yes, it would be unusual because less than 5% of all such samples have means less than 91.Yes, it would be unusual because more than 5% of all such samples have means less than 91.

Answer 1

Solution :

Given that ,

mean = = 90

standard deviation = = 3

n = 36

a) has an approximately normal distribution with,

= = 90  

= / n = 3 / 36 = 0.5

b) = 91

z = - ) /

z = 91 - 90 / 0.5

z = 2.00

c) 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 91.