Normal Distributions: Finding Probabilities

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A survey indicates that for each trip to the supermarket, a shopper spends an average of 45 minutes with a standard deviation of 12 minutes in the store. The length of time spent in the store is normally distributed and is represented by the variable x. A shopper enters the store. Find the probability that the shopper will be in the store for between 24 and 54 minutes.

Find the probability that the shopper will be in the store more than 39 minutes. (Recall µ = 45 minutes and σ = 12 minutes)

If 200 shoppers enter the store, how many shoppers would you expect to be in the store for more than 39 minutes?

Triglycerides are a type of fat in the bloodstream. The mean triglyceride level in the United States is 134 milligrams per deciliter. Assume the triglyceride levels of the population of the United States are normally distributed, with a standard deviation of 35 milligrams per deciliter. You randomly select a person from the United States. What is the probability that the person’s triglyceride level is less than 80?