Question

Suppose x has a distribution with a mean of 20 and a standard deviation of 9. Random samples of size n = 36 are drawn.

(a) Describe the x bar distribution. x bar has a Poisson distribution. x bar has a geometric distribution. x bar has an unknown distribution. x bar has an approximately normal distribution. x bar has a binomial distribution. x bar has a normal distribution. Compute the mean and standard deviation of the distribution. (For each answer, enter a number.) mu sub x bar = mu sub x bar = sigma sub x bar = sigma sub x bar =

(b) Find the z value corresponding to x bar = 17. (Enter an exact number.) z =

(c) Find P(x bar < 17). (Enter a number. Round your answer to four decimal places.) P(x bar < 17) = P(x bar < 17) (d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 17? Explain. No, it would not be unusual because less than 5% of all such samples have means less than 17. Yes, it would be unusual because less than 5% of all such samples have means less than 17. Yes, it would be unusual because more than 5% of all such samples have means less than 17. No, it would not be unusual because more than 5% of all such samples have means less than 17.

Answer 1

a)
x bar has an approximately normal distribution.
xbar = 20
s = 9/sqrt(36) = 1.5

b)
z = (17 - 20)/1.5 = -2

c)
P(X < 17) = P(z < -2)
= 0.0228
d)
No, it would not be unusual because less than 5% of all such samples have means less than 17