Question

Suppose that the mean weight for men 18 to 24 years old is 170 pounds, and the standard deviation is 20 pounds. In each part, find the value of the standardized score (z-score) for the given weight.a. 200 pounds.b. 140 pounds.c. 170 pounds.d. 230 pounds.

Answer 1

a)
`Z = 1.5`

b)
`Z = -1.5`

c)
`Z = 0`

d)
`Z = 3`

Explanation:

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

In this problem, we have that:

`\mu = 170, \sigma = 20`

a. 200 pounds.

`Z = (X - \mu)/(\sigma)`

`Z = (200 - 170)/(20)`

`Z = 1.5`

b. 140 pounds.

`Z = (X - \mu)/(\sigma)`

`Z = (140 - 170)/(20)`

`Z = -1.5`

c. 170 pounds.

`Z = (X - \mu)/(\sigma)`

`Z = (170 - 170)/(20)`

`Z = 0`

d. 230 pounds.

`Z = (X - \mu)/(\sigma)`

`Z = (230 - 170)/(20)`

`Z = 3`