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**1. **The following probability distribution table is for the random variable, x, the number of children under the age of 20 years in households of a small town. Remember to show all work to answer the following questions.

**x **P(x)

0 0.17

1 0.45

2 0.20

3 0.12

4 0.06

> 4 0.00

a) Determine the mean of .

b) Determine the standard deviation of .

c) Find the probability of a household consisting of 3 or more children under the age of 20

Round all answers *a - c* to 2 decimal places.

**2. **A certain strain of bacteria occurs in all raw milk. Tests of uncontaminated raw milk conducted by the Health Department found that the bacteria count per milliliter is normally distributed with a mean of 3000 and standard deviation of 300.

In a large commercial dairy, the health inspector investigates 51 random containers of the uncontaminated raw milk produced each day. At the end of the day, the bacteria count in each of the 51 containers is averaged to obtain the sample mean bacteria count.

a) What is the probability of finding a sample mean bacteria count between 2902 and 3098 in a milliliter of uncontaminated raw milk? Round your answer to 3 decimal places.

b) Suppose the 51 samples taken by the inspector have a mean bacteria count that is *not *between 2902 and 3098. If you were the inspector, what would be your comment on this situation? Would you approve of or reject the milk? Explain thoroughly.

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