Suppose x has a distribution with a mean of 70 and a standard deviation of 44. Random samples of size n = 64 are drawn.
(a) Describe the distribution.
The distribution has an approximately normal distribution.
Compute the mean and standard deviation of the distribution. (For each answer, enter a number.)
μ sub x bar = 70
σ sub x bar = 44/√64 = 5.5
(b) Find the z value corresponding to x bar = 59. (Enter an exact number.)
z = (59 - 70) / 5.5 = -11/5.5 = -2
(c) Find P(x bar < 59). (Enter a number. Round your answer to four decimal places.)
P(x bar < 59) = P(z < -2) = 0.0228
(d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 59? Explain.
Yes, it would be unusual because less than 5% of all such samples have means less than 59.