Question

Best Electronics offers a “no hassle” returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 8.7 per day and the standard deviation is 1.85 per day. Refer to the table in Appendix B.1. a. In what percentage of the days 7 or fewer customers returning items? (Round z-score computation to 2 decimal places and the final answer to 2 decimal places.) Percentage % b. In what percentage of the days between 10 and 15 customers returning items? (Round z-score computation to 2 decimal places and the final answer to 2 decimal places.) Percentage % c. Is there any chance of a day with no returns?

Answer 1

Solution :

Given that ,

mean = = 8.7

standard deviation = = 1.85

(a)

P(x 7) = P((x - ) / (7 - 8.7) / 1.85)

= P(z -0.92)

Using standard normal table

= 0.1788

Answer = 17.88%

(b)

P(10 < x < 15) = P((10 - 8.7)/ 1.85) < (x - ) /  < (15 - 8.7) / 1.85) )

= P(0.70 < z < 5.03)

= P(z < 5.03) - P(z < 0.70)

= 1 - 0.758

= 0.242

Answer = 24.2%

(c)

P(x < 0) = P((x - ) / < (0 - 8.7) / 1.85)

= P(z < -4.70)

= 0

Answer = 0%