Question

The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.68 inches.The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.52 inches.a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?z = ________b) What percentage of men are SHORTER than 6 feet 3 inches? Round to nearest tenth of a percent.__________%c) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?z =_________e) Who is relatively taller: a 6'3" American man or a 5'11" American woman? Defend your choice in a meaningful sentence.

Answer 1

a) z-score for men is 2.13. b) percentage of men shorter than 6 feet 3 inches is 98%. c) z-score for women is 2.46. d) The American woman is relatively taller.

Explanation:

The z-score is calculate by the difference between the value and the mean divided by the standard deviation. For men, z-score will be 2.13 and for women it will be 2.46. If you reference to the distribution graph, a z-score of about 2 is approximately 98% of cumulative percentage. This means that 98% of men is shorter than 6 feet 3 inches tall. The American woman of 5'11" is relatively taller than a men of 6'3" because of its z-score. Since it is closer to 3, the percentage of women shorter than 5'11" will be over 98% and lower than 99%, which is already taller than the value found for men of 6'3".