Question

In a class there are 20 students: 3 are 5' 6", 5 are 5'8", 4 are 5'10", 4 are 6', and 4 are 6' 2". A student is chosen at random. What is the student's expected height?

Answer 1

5'10"

Explanation:

Converting the heights to inches we have 66, 68, 70, 72 and 74 inches.

Prob( Choosing 66 student) = 3/20

Prob( Choosing 68" .. ) = 5/20 = 1/4.

Prob( Choosing 70" ... ) = 4/20 = 1'5.

Prob( Choosing 72' . ... ) = 4/20 = 1/5.

Prob (Choosing 74" .... ) = 4/20 = 1/5.

Expected height = 3/10 *66 + 1/4*68 + 1/5*70 + 1/5*72 + 1/5*74.

= 701/10

= 70.1

= 5'10"

Answer 2

The student's expected height is 5' 10.1".

Explanation:

In a class there are 20 students: 3 are 5' 6", 5 are 5'8", 4 are 5'10", 4 are 6', and 4 are 6' 2".

First we will convert these heights to inches like:

12 inches = 1 feet

5' 6" =
`60+6` = 66

5'8" =
`60+8` = 68 and so on.

So, we get following heights in inches:

66, 68, 70 ,72, 74

Expected height = (3/20)66 + (5/20)68 + (4/20)70 + (4/20)72 + (4/20)74 = 70.1 inches.

Or in feet, it will be : 5' 10.1"