Question

1. You have 10 yellow socks and 14 brown socks. You randomly select 2 socks. What is the probability they are both brown? Round to the nearest thousandth.

A. .33

B. .65

C. .44

D. .51

e. none of the above

2. The height of adult males in the U.S is normally distributed with a mean of 5.75 feet and a standard deviation of .2 feet. What percent of the adult male population has a height between 5.55 feet and 5.95 feet? Round to the nearest percent.

A. 90

B 60

C. 40

D. 16

E. 68

Answer 1

1)

2 brown socks are selected from 14 brown socks by ¹⁴C₂ ways .

Total number of ways to select 2 socks from 24(24+10) total socks by ²⁴C₂ ways.

Therefore,

P( both brown socks) = ¹⁴C₂ / ²⁴C₂

= 0.33

b)

Given,

= 5.75, = 0.2

We convert this to standard normal as

P( X < x) = P( Z < x - / )

We have to calculate P( 5.55 < X < 5.95) = ?

P( 5.55 < X < 5.95) = P( X < 5.95) - P( X < 5.55)

= P( Z < 5.95 - 5.75 / 0.2) - P( Z < 5.55 - 5.75 / 2)

= P( Z < 1) - P( Z < -1)

= 0.8413 - ( 1 - 0.8413)

= 0.68