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

= $\frac{30}{100}\times30 +\frac{25}{100}\times32+ \frac{10}{100}\times34+ \frac{10}{100}\times36 +\frac{10}{100}\times38+ \frac{15}{100}\times40$

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

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