Question

Suppose x has a distribution with a mean of 80 and a standard deviation of 20. 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 distribution with mean μx = and standard deviation σx = . (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 64 from the x distribution to have a sample mean less than 75? Explain. Yes, it would 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. No, it would not be unusual because more than 5% of all such samples have means less than 75. Yes, it would be unusual because less than 5% of all such samples have means less than 75.

Answer 1

Solution :

Given that ,

mean = = 80

standard deviation = = 20

n = 64

a) x distribution is an approximately normal with,

=    = 80

= / n = 20 / 64 = 2.5

b) = 75

Using z-score formula,

z = - /

z = 75 - 80 / 2.5

z = -2.00

c) P( < 75) = P(( - ) / < (75 - 80) / 2.5)

= 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 75.