Question

Student Group	Mean GPA (μ)	Standard deviation (σ) of GPA
All students	3.33	0.53
Female students	3.40	0.50
Male students	3.23	0.54

1.) Which would be more likely: a female student with a high school GPA of at least 4.25, or a male student with a high school GPA of at least 4.00? Solve this problem using the Standard Normal Table (Z table). Show all work and explain your reasoning.

2.) What is the probability that a randomly selected male student had a high school GPA between 3.25 and 3.75? Solve this problem using the Standard Normal Table (Z table). Show all work and provide the probability as a decimal rounded to four decimal places.

Answer 1

1)

Z score for female student with a high school GPA of 4.25 = (4.25 - 3.40)/0.50 = 1.7

Probability of a female student with a high school GPA of at least 4.25 = P(z > 1.7) = 0.0446 (Using Z table)

Z score for male student with a high school GPA of 4.00 = (4.00 - 3.23)/0.54 = 1.43

Probability of a male student with a high school GPA of at least 4.00 = P(z > 1.43) = 0.0764 (Using Z table)

As, probability of a male student with a high school GPA of at least 4.00 is greater, it is more likely.

2)

Z score for male student with a high school GPA of 3.25 = (3.25 - 3.23)/0.54 = 0.04

Z score for male student with a high school GPA of 3.75 = (3.75 - 3.23)/0.54 = 0.96

Probability that a randomly selected male student had a high school GPA between 3.25 and 3.75

= P(0.04 < Z < 0.96) = P(Z < 0.96) - P(Z < 0.04)

= 0.8315 -  0.5160 (Using Z table)

= 0.3155