Question

Suppose x has a distribution with a mean of 90 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 distribution with mean μx = and standard deviation σx = . (b) Find the z value corresponding to x = 99. z = (c) Find P(x < 99). (Round your answer to four decimal places.) P(x < 99) = (d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 99? Explain. No, it would not be unusual because less than 5% of all such samples have means less than 99. No, it would not be unusual because more than 5% of all such samples have means less than 99. Yes, it would be unusual because less than 5% of all such samples have means less than 99. Yes, it would be unusual because more than 5% of all such samples have means less than 99

Answer 1

a)

= = 90

= / sqrt(n)

= 27 / sqrt(36)

= 4.5

b)

z-score = (x - ) /

= ( 99 -90) / 4.5

= 2

c)

P(X < 99) = P(Z < 2)

= 0.9772 (From Z table)

d)

No, it would not be unusual because more than 5% of all such samples have means less than 99