In a survey of women in a certain country (ages 20 - 29), the mean height was 62

Question

In a survey of women in a certain country (ages 20 - 29), the mean height was 62.6 inches with a standard deviation of 2.69 inches. Answer the following questions about the specified normal distribution. (a) What height represents the 95th percentile? (b) What height represents the first quartile? (a) The height that represents the 95th percentile is ___ inches. (Round to two decimal places as needed.) (b) The height that represents the first quartile is ___ inches. (Round to two decimal places as needed.)

Explanation / Answer

a) For 95th percentile, z = 1.645

Hence,

Height that represents 95th percentile = 62.6 + 1.645*2.69 = 67.03

b) For first quartile, z = -0.67

Hence,

Height that represents the first quartile = 62.6 - 0.67*2.69 = 60.80

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