Question

**Directions**: 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.

**Part 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 points)**Based on your answer to part (a), how do you feel about your uncle’s story? Explain.

**Part 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 3.6 lb and 5.0 lb. What percent of mackerel will this
restaurant be willing to purchase? Round your answer to 2 digits
after the decimal.

**Part 3. (5 points)** A fishing contest gives
prizes for anyone who catches an Atlantic mackerel that is in the
top 10% of weights. What is the cut off weight for earning an
award? Round your answer to two digits after the decimal.

Answer #1

b. It is very difficult to believe uncle's story story since probability getting mackerel with weight 7lb or more is very low.

Part 2:

Part 3:

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
(5 points) Your uncle claims that he once
caught a 7 lb. mackerel on a fishing trip. What is the probability
of finding a...

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