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return policy and label weight

1) Best Electronics Inc. offers a "no hassle" returns policy. The number of items returned per day follows the normal distribution. The mean number of customers returns is 10.3 per day and the standard deviation is 2.25 per day.

a. In what percent of the days are there 8 or fewer customers returning items?

b. In what percent of the days are between 12 and 14 customers returning items?

c. Is there any chance of a day with no returns?

2) The weights of canned hams processed at Henline Ham Company follow the normal distribution, with a mean of 9.20 pounds and a standard deviation of .25 pounds. The label weight is given as 9.00 pounds

a. What proportion of the hams actually weigh less than the amount claimed on the labe?

b. The owner, Glen Henline, is considering two proposals to reduce the proportion of hams below label weight. He can increase the mean weight to 9.25 and leave the standard deviation the same, or he can leave the mean weight at 9.20 and reduce the standard deviation from .25 pounds to .15. Which change would you recommend?

Solution Preview

mean, mu = 10.3/day
standard deviation, SD = 2.25 /day

probability of x = 8 or lower
p(x<= 8)
z = (x - mu)/SD = (8-10.3)/2.25 = -1.02

P(Z <= z) = P (Z <= -1.02) == 0.5 - P(Z <= 1.02) = 0.5 - 0.3461 = 0.1539 == 15.39%
[From Normal table, with right half, P(Z <= 1.02) = 0.3461]

In 15.39% of days, 8 or fewer customers return items. --Answer

probability of returning between x1 = 12 and x2 = 14
P( x1 <= X <= x2) == P(z1 ...

Solution Summary

Two problems are solved here, first one return policy related statistics, and the second one packaging weight variation related.