Question

Scores of students in a large Statistics class are normally distributed with a mean of 75 points and a standard deviation of 5 points.

1. Find the probability that a student scores more than 80 points
2. If 100 students are picked at random, how many do you expect to score below 70 points?
3. If top 10% of students obtain an A grade, how much should a student obtain to get an A grade.
4. Suppose four students are picked at random, find the probability that the average score of those four students is more than 80 points.

Answer 1

µ = 75

σ = 5

x = 80

z = (x - µ)/σ = (80 - 75)/5 = 1

The probability that a student scores more than 80 points is 0.1587.

If 100 students are picked at random, 16 would score below 70 points.

z = 1.28

1.28 = (x - 75)/5

x = 1.28*5 + 75 = 81.4

81.4 should a student obtain to get an A grade.

z = (x - µ)/σ/√n = (80 - 75)/5/√4 = 2

The probability that the average score of those four students is more than 80 points is 0.0228.

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