Question

Consider the approximately normal population of heights of female college students with a mean μ = 69.5 inches and a standard deviation σ = 3 inches. A random sample of 36 females is obtained.

a. What is the probability that an individual height of a female college student, x, is at least 70 inches? Mark and label the mean μ along with the x value then shade the area defining the probability of interest on the graph A. Mark and label the z-score then shade the area defining the probability of interest on the graph B.

b. What is the probability that the sample mean height of female college students, ?̅, is at least 70 inches? Mark and label the mean ?x̅ along with the ?̅ value then shade the area defining the probability of interest on the graph A. Mark and label the z-score then shade the area defining the probability of interest on the graph B.

Answer 1

Solution:

Given:  The heights of female college students are approximately normal with a mean μ = 69.5 inches and a standard deviation σ = 3 inches.

Sample size= n = 36

Part a) Find:

Find z score for x = 70

Thus

Look in z table for z = 0.1 and 0.07 and find corresponding area.

P( Z < 0.17) = 0.5675

thus

Part b)

thus

Look in z table for z = 1.0 and 0.00 and find corresponding area.

P( Z < 1.00) = 0.8413

thus