Meredith Jones knows that the heights of male undergraduate students at her scho

Question

Meredith Jones knows that the heights of male undergraduate students at her school are normally distributed with a mean of 70 inches and a standard deviation of 4 inches, and that heights of female undergraduate students are normally distributed with a mean of 67 inches and a standard deviation of 3 inches. She knows, furthermore, that male students outnumber female students 3 to 1 at her school. a) What is the probability that a randomly selected female undergraduate is more than 70 inches tall? b) Meredith is 72 inches tall. She has been randomly assigned another undergraduate (who could be male or female) as her lab partner. What is the probability that her lab partner is taller than she?

Explanation / Answer

A) P(X > 70)

= P((x - mean)/SD > (70 - mean)/SD)

= P(Z > (70 - 67)/3)

= P(Z > 1)

= 1 - P(Z < 1)

= 1 - 0.8413 = 0.1587

B) P(x > 72)

= P((x - mean)/SD > (72 - mean)/SD)

= P(Z > (72 - 67)/3)

= P(Z > 1.67)

= 1 - P(Z < 1.67)

= 1 - 0.9525 = 0.0475

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