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.
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
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