Question

: In a survey of 18 -year-old males, the mean weight was 156.8 pounds with a standard deviation of 48.2 pounds. (a) What weight represents the 98 th percentile? (b) What weight represents the 36 th percentile? (c) What weight represents the third quartile?

Answer 1

(a) 255.8028 pounds

(b) 139.5444 pounds

(c) 189.2868 pounds

Explanation:

μ = 156.8

σ = 48.2

(a)

P = 0.98 → Z = 2.054

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

`2.054 = (x-156.8)/(48.2)`

`2.054*48.2=x-156.8`

`x=99.0028+156.8`

`=255.8028\ pounds`

(b)

P = 0.36 → Z = -0.358

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

`-0.358 = (x-156.8)/(48.2)`

`-0.358*48.2=x-156.8`

`x=-17.2556+156.8`

`=139.5444\ pounds`

(c)

P = 0.75 → Z = 0.674

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

`0.674 = (x-156.8)/(48.2)`

`0.674*48.2=x-156.8`

`x=32.4868+156.8`

`=189.2868\ pounds`