Question1

You collected a sample of 100 observations. You are certain that the sample came from a Normal distribution with a standard deviation of 5. However, you are not sure about the mean, denoted as mu, of that Normal distribution. Therefore, you are going to perform a hypothesis test.

The mean of the sample is 48.26610496.

Your null hypothesis is mu equals 50 and the alternative hypothesis is non-directional (i.e., mu does not equal 50).

What is the significance value (i.e., p-value)? Please round your answer to the fourth decimal place.

Question2

The random variable X follows a Normal distribution with a mean of 100 and a standard deviation of 5.

What is the value of b if the probability Pr(97.3780 < X < b) = 0.5?Please round your answer to the fourth decimal place.

Question3

Coliform bacteria are randomly distributed in a certain Arizona river at an average concentration of 1 bacteria per 20cc of water. If we draw from the river a test tube containing 30cc of water, what is the probability that the sample contains exactly 4 coliform bacteria?Please round your answer to the fourth decimal place.