Question

Consider the approximately normal population of heights of male college students with mean μ = 72 inches and standard deviation of σ = 8.6 inches. A random sample of 14 heights is obtained.

(e) Find the standard error of the x distribution. (Give your answer correct to two decimal places.)


(f) Find P(x > 69). (Give your answer correct to four decimal places.)


(g) Find P(x < 67). (Give your answer correct to four decimal places.)

Answer 1

Solution: Given that mean μ = 72 inches and standard deviation of σ = 8.6 inches, for n = 14

(e) standard error = σ/sqrt(n) = 8.6/sqrt(14) = 2.2984 = 2.30 (rounded)

(f) P(X > 69) = P((X-μ)/(σ/sqrt(n)) > (69-72)/(8.6/sqrt(14)))
= P(Z > -1.3052)
= 0.9049

(g) P(X < 67) = P((X-μ)/(σ/sqrt(n)) < (67-72)/(8.6/sqrt(14)))
= P(Z < -2.1754)
= 0.0146