Question

A clothing store has a section of jeans on sale. There is a 30% chance of picking a pair with a 30-inch inseam; a 25% chance of picking a pair with a 32-inch inseam; a 10% chance of picking a pair with a 34-inch inseam; a 10% chance of picking a pair with a 36-inch inseam; a 10% chance of picking a pair with a 38-inch inseam; and a 15% chance of picking a pair with a 40-inch inseam. Find the expected value of the inseam length of the jeans.

33

33.4

33.8

35

Answer 1

The expected value of the inseam length of the jeans is found as

30% of 30+ 25% of 32+ 10% of 34+ 10% of 36 + 10% of 38 + 15% of 40

=
`(30)/(100)*30 +(25)/(100)*32+ (10)/(100)*34+ (10)/(100)*36 +(10)/(100)*38+ (15)/(100)*40`

=
`9+8+3.4+3.6+3.8+6=33.8`

Hence, the third option 33.8 is the correct expected value.