Question

Suppose certain coins have weights that are normally distributed with a mean of 5.629 g and a standard deviation of 0.056 g. A vending machine is configured to accept those coins with weights between 5.559 g and 5.699 g.

a. If 280 different coins are inserted into the vending​ machine, what is the expected number of rejected​ coins?

Answer 1

From normal distribution, we calculate the proportion of coins with a weight between 5.559 g and 5.699. We will use that proportion as a parameter of the binomial distribution.

We need to compute Pr (5.559 ≤ X ≤ 5.699). The corresponding z-values needed to be computed are:

Therefore, we get:

The proportion of coins that are accepted in the vending machine is 0.7887.

Therefore, the proportion of coins that are rejected in the vending machine is 1 - 0.7887 = 0.2113

Hence, the expected number of rejected​ coins is 0.2113 * 280 = 59.164 59 coins.