Question

Suppose that the level of education for everyone in the population has a normal distribution. Assume that the mean level of education is 12 years (HS degree) and the standard deviation is 2 years.

1. Provide the Z scores for the following years of education: 7.5, 10, 13.5, and 15.
2. Suppose three members of the population are selected at random. Their Z scores are -1, 0.5, and 2.0. How many years of education does each person have?
3. What percentage of the population has between 11.5 and 13 years of education?

Answer 1

Given that, mean (μ) = 12 years and

standard deviation = 2 years

a) For x = 7.5

=> Z-score = -2.25

For x = 10

=> Z-score = -1

For x = 13.5

=> Z-score = 0.75

For x = 15

=> Z-score = 1.5

b) For z = -1

=> x = 10 years

For z = 0.5

=> x = 13 years

For z = 2.0

=> x = 16 years

c) We want to find, P(11.5 < X < 13)

In percentage : 0.2902 * 100 = 29.02%

Therefore, required percentage is 29.02%

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