math 146 I need help

Question

The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.62 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 2.56 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 = 

d) What percentage of women are TALLER than 5 feet 11 inches? Round to nearest tenth of a percent.

%

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

Notice that the main body of the problem tells you the mean and standard deviation for men, and separately gives you the mean and standard deviation for women. For each part, you're calculating the z score for a man or the z score for a woman. Either the men's mean and standard deviation will be used or the women's mean and standard deviation are used in the calculation of z=(x-μ)/σ.

I would suggest that you convert all heights to inches only to make the math a little simpler. For example, a height of 5'7" would be 5*12+7=67".

For the probability questions, use the z-score table to find your answer. The ones place and the first decimal you find on the far left of the table, while the second decimal place you'll find on the far top. The probability you're looking for is where the left number you found and the top number you found meet.

Keep in mind that this probability is the probability of that z-value or less. If you're looking for that z value or more, do 1-(Ans).