Question

The amount of filling in a Doughiest Donut Boston cream donut follows a Normal distribution, with a mean of 3 ounces and a standard deviation of 0.4 ounce. A random sample of 36 donuts is selected every day and measured. What is the probability the mean weight will exceed 3.1 ounces?

Answer 1

The probability the mean weight will exceed 3.1 ounces is 0.0668

Explanation:

We have a random sample of size n = 36 measures which comes from a normal distribution with a mean of 3 ounces and a standard deviation of 0.4 ounces. Then, we know that the mean weight is also normally distributed with the same mean of 3 ounces and a standard deviation of
`0.4/√(36) = 0.4/6`. The z-score associated to 3.1 is (3.1-3)/(0.4/6) = 1.5. We are looking for P(Z > 1.5) = 0.0668, i.e., the probability the mean weight will exceed 3.1 ounces is 0.0668