SOLUTION: suppose certain coins weights that are normally distributed with a mean of 5.285 g and a standard deviation of 0.066g. A vending machine is configured to accept those coins with w

Question 1119811: suppose certain coins weights that are normally distributed with a mean of 5.285 g and a standard deviation of 0.066g. A vending machine is configured to accept those coins with weights between 5.175g and 5.395 g.
a. If 250 different coins are inserted into the vending machine, what is the expected number of rejected coins?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The standard error of the sample of 250 is sigma/sqrt (n) or 0.066/sqrt (250), and that is 0.0042
The rejection region is 0.110 from the mean in both directions.
The z-value for the rejection region is +/- 0.110/0.0042=2.62
This has a probability (both tails) of 0.0088.
For 250 coins, 250*0.0088=2.2
2 coins would be expected to be rejected.
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