Question

In the mailroom, the mean weight of a letter 25.0 grams. The standard deviation is 0.1 grams. A first-class stamp is sufficient postage to mail a letter with a maximum weight of 28 grams. On a given day, the post office in downtown Hillsboro processes an average of 12,370 pieces of mail with a first-class stamp as postage. If the letter weight is normally distributed, approximately how many of these letters will need additional postage?

Answer 1

Let X be the random variable denoting the weight of a letter.

So X is normally distributed with mean 25 grams and standard deviation 0.1 gram

so X~N(25,0.12)

A first-class stamp is sufficient postage to mail a letter with a maximum weight of 28 grams

so the probability that a randomly selected letter will require additional postage is

P[X>28]=P[(X-25)/0.1>(28-25)/0.1]=P[Z>3/0.1]=P[Z>30]=0.0001

hence expected number of letters among 12,370 will require additional postage is 12,370*0.0001~~1 [answer]