Question

Suppose x has a distribution with a mean of 70 and a standard deviation of 15. 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 an unknown a geometric an approximately normal a normal a Poisson distribution with

mean μ_x =

and

standard deviation σ_x =  .

(b) Find the z value corresponding to

x = 75.

z =

(c) Find

P(x < 75).

(Round your answer to four decimal places.)

P(x < 75) =

(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 75? Explain.

Yes, it would be unusual because less than 5% of all such samples have means less than 75.No, it would not be unusual because more than 5% of all such samples have means less than 75.    No, it would not be unusual because less than 5% of all such samples have means less than 75.Yes, it would be unusual because more than 5% of all such samples have means less than 75.

Answer 1

Solution :

Given that ,

mean = = 70

standard deviation = = 15

n = 36

a) Approximately normal

mean =   = 70

standard deviation = / n = 15/ 36 = 2.5

b) x = 75

z = x-u /

z = 75 - 70 / 15 = 0.33

z = 0.33

c)P(x < 75).

= P[(x - ) / < (75-70) /15 ]

= P(z < 0.33)

=0.6293

probability = 0.6293

d) sample mean less than 75

P( < 75 ) = P(( - ) / < (75-70) /2.5 )

= P(z < 2)

= 0.9772

probability = 0.9772

No, it would not be unusual because more than 5% of all such samples have means less than 75