Question

The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.61 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 2.51 inches. a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)

Answer 1

1.99

Explanation:

We have been given the heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.61 inches. We are asked to find the z-score of height of man with 6 feet 3 inches.

We will use z-score formula to solve our given problem.

`z=(x-\mu)/(\sigma)`, where,

z = z-score,

x = Sample score,

`\mu` = Mean,

`\sigma` = Standard deviation,

6 feet 3 inches = 72+3 inches = 75 inches

`z=(75-69.8)/(2.61)`

`z=(5.2)/(2.61)`

`z=1.99233716475`

`z\approx 1.99`

Therefore, the z-score for the man with height of 6 feet 3 inches is 1.99.