Question

For full credit, be sure to include a sketch of the normal distribution, relevant formulas/computations, and appropriate probability notation.

Background Information

Atlantic mackerel are fish that grow to an average weight of 4.1 lb., with a standard deviation of 1.1 lb. We can assume that the weights of Atlantic mackerel are normally distributed.

Exercises

Problem 1

1. (5 points) Your uncle claims that he once caught a 7 lb. mackerel on a fishing trip. What is the probability of finding a mackerel that is 7 lb. or larger? Round your answer to 4 digits after the decimal.
2. (2 points) Based on your answer to part (a), how do you feel about your uncle’s story? Explain.

Problem 2. (5 points) A restaurant purchases Atlantic mackerel to cook and serve. To avoid complaints from customers, the restaurant does not want too much variety in fish weight. They will only purchase mackerel that weigh between 3.5 lb. and 4.9 lb. What percent of mackerel will this restaurant be willing to purchase? Round your answer to 2 digits after the decimal.

Problem 3. (5 points) A fishing contest gives prizes for anyone who catches an Atlantic mackerel that is in the top 5% of weights. What is the cut off weight for earning an award? Round your answer to two digits after the decimal.

Answer 1