Question

The heights of adult men in America are normally distributed, with a mean of 69.4 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.2 inches and a standard deviation of 2.59 inches.

a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? If a women if 5 feet 11 inches tall, what is her z-score?? (To two decimal places)

Answer 1

Explanation:

Use: z-score = (x - μ)/σ

Convert the height to inches: x_man = 6 ft 3 in. = 6(12) + 3 = 75 in.

z_man = (75 - 69.2)/2.66 = 2.18 --> from a z-table --> .9854(100) = 98.54%

Convert the height to inches: x_woman = 5 ft 11 in. = 5(12) + 11 = 71 in.

z_woman = (71 - 64.3)/2.58 = 2.60 --> from a z-table --> .9953(100) = 99.53%

Answers:

a) z_man = 2.18

Use: z-score = (x - μ)/σ

Convert the height to inches: x_man = 6 ft 3 in. = 6(12) + 3 = 75 in.

z_man = (75 - 69.2)/2.66 = 2.18 --> from a z-table --> .9854(100) = 98.54%

Convert the height to inches: x_woman = 5 ft 11 in. = 5(12) + 11 = 71 in.

z_woman = (71 - 64.3)/2.58 = 2.60 --> from a z-table