Question

Suppose x has a distribution with a mean of 70 and a standard deviation of 27. 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 binomial a geometric a Poisson a normal an approximately normal an unknown distribution with

mean μ_x =

and

standard deviation σ_x =  .

(b) Find the z value corresponding to

x = 61.

z =

(c) Find

P(x < 61).

(Round your answer to four decimal places.)

P(x < 61) =

(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 61? Explain.

No, it would not be unusual because more than 5% of all such samples have means less than 61.Yes, it would be unusual because less than 5% of all such samples have means less than 61.    Yes, it would be unusual because more than 5% of all such samples have means less than 61.No, it would not be unusual because less than 5% of all such samples have means less than 61.

Answer 1

Solution :

Given that ,

mean = = 70

standard deviation = = 27

n = 36

a) x has an approximately normal distribution with,

=   = 70

= / n = 27 / 36 = 4.5

b) Using z-score formula,

= 61

z = - /

z = 61 - 70 / 4.5

z = -2.00

c) P( < 61 ) = P(( - ) / < (61 - 70 ) / 4.5)

= 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 61.