Suppose the amount of milk produced daily by the whole population of Nordic Red dairy cows is Normally distributed with a mean of approximately 28.2 kilograms and a standard deviation of approximately 3.71 kilograms.

a. What percentage of these dairy cows do we expect to produce between 25 and 29 kilograms of milk daily? To show your work: Write down which calculator/program you are using and what values you are entering into the calculator)

b. Find the amount of milk produced by the lowest 15% producing dairy cows. Include units in your answer. (To show your work: Write down which calculator program your are using and what values you are entering into the calculator).

C. Give the mean and standard deviation of the normal model that would be used to approximate the sampling distribution of the sample mean for a random of 40 Nordic Red dairy cows. Include units in your answer.

d. Sketch and clearly label and the normal model for the sampling distribution of the sample mean from part c, based on the 68-99.7 Rule Be sure to label your axis with what the variable in the sampling distribution represents.

e. Find the probability that a random sample of 40 Nordic Red dairy cow produces an average amount of milk greater than 29 kilograms daily. (To show your work: Write down which calculator/program you are using and what values you are entering into the calculator)