the heights of adult men in america are normally distributed, with a mean of 69.1 inches and a standard…

the heights of adult men in america are normally distributed, with a mean of 69.1 inches and a standard deviation of 2.65 inches. the heights of adult women in america are also normally distributed, but with a mean of 64.6 inches and a standard deviation of 2.53 inches.\na) if a man is 6 feet 3 inches tall, what is his z - score (to two decimal places)?\nz =\n\nb) if a woman is 5 feet 11 inches tall, what is her z - score (to two decimal places)?\nz =\n\nc) who is relatively taller?\nthe 5 foot 11 inch american woman\nthe 6 foot 3 inch american man\nsubmit question

the heights of adult men in america are normally distributed, with a mean of 69.1 inches and a standard deviation of 2.65 inches. the heights of adult women in america are also normally distributed, but with a mean of 64.6 inches and a standard deviation of 2.53 inches.\na) if a man is 6 feet 3 inches tall, what is his z - score (to two decimal places)?\nz =\n\nb) if a woman is 5 feet 11 inches tall, what is her z - score (to two decimal places)?\nz =\n\nc) who is relatively taller?\nthe 5 foot 11 inch american woman\nthe 6 foot 3 inch american man\nsubmit question

Answer

Explanation:

Step1: Convert heights to inches

1 foot = 12 inches. A man 6 feet 3 inches tall is (6\times12 + 3=75) inches. A woman 5 feet 11 inches tall is (5\times12+11 = 71) inches.

Step2: Calculate man's z - score

The z - score formula is (z=\frac{x-\mu}{\sigma}), where (x) is the value, (\mu) is the mean and (\sigma) is the standard deviation. For men, (\mu = 69.1) and (\sigma=2.65). So (z_{man}=\frac{75 - 69.1}{2.65}=\frac{5.9}{2.65}\approx2.22).

Step3: Calculate woman's z - score

For women, (\mu = 64.6) and (\sigma = 2.53). So (z_{woman}=\frac{71-64.6}{2.53}=\frac{6.4}{2.53}\approx2.53).

Step4: Compare z - scores

Since (2.53>2.22), the woman is relatively taller.

Answer:

a) (z = 2.22) b) (z = 2.53) c) The 5 foot 11 inch American woman