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Question

Suppose that the heights of adult women in the United States are normally distributed with a mean of 63.5

 inches and a standard deviation of 2.3

 inches. Maria is taller than 90%

 of the population of U.S. women. How tall (in inches) is Maria? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

Answer 1

90% of the population is the same as the probability (0.90). Use the z-score table from the textbook or online to find the z-score for the given probability.

The z-score for the probability of 0.90 is about 1.281.

The raw score (X) represents Maria's height. To find X, we need the z-score formula with the given information from the problem.

z = (X - μ) / σ ⇒ 1.281 = (X - 63.5) / 2.3 ⇒ 2.9463 = X - 63.5 ⇒ X = 66.4463 ≈ 66.4

Maria is about 66.4 inches tall.