Section 5 2 Normal Distributions Finding Probabilities Example

Section 5. 2 Normal Distributions: Finding Probabilities

Example 1 A survey indicates that people use their computers an average of 2. 4 years before upgrading to a new machine. The standard deviation is 0. 5 year. A computer owner is selected a random. Find the probability that he or she will use it for less than 2 years before upgrading. Assume that the variable x is normally distributed. There is a 21. 19% chance owners will upgrade in less than 2 years.

Example 2 A Ford Focus manual transmission gets an average of 27 miles per gallon (mpg) in city driving with a standard deviation of 1. 6 mpg. A Focus is selected at random. What is the probability that it will get more than 31 mpg? Assume that gas mileage is normally distributed. There is a. 62% chance the car gets more than 31 mpg.

Example 3 A survey indicates that for each trip to the supermarket, a shopper spends an average of µ = 45 minutes with a standard deviation of σ = 12 minutes. The length of time spent in the store is normally distributed and is represented by the variable x. A shopper enters the store. (a. ) Find the probability that the shopper will be in the store for each interval of time listed below. (b. ) If 200 shoppers enter the store, how many shoppers would you expect to be in the store for each interval of time listed below ? Between 24 and 54 minutes There is a 73. 33% chance that a person will be in the store between 24 and 54 minutes. More than 39 minutes There is a 69. 15% chance that a person will be in the store for more than 39 minutes. Between 33 and 60 minutes There is a 73. 57% chance that a person will be in the store between 33 and 60 minutes.

Example 4 Assume that cholesterol levels of men in the US are normally distributed, with a mean of 215 milligrams per deciliter and a standard deviation of 25 milligrams per deciliter. You randomly select a man from the US. What is the probability that his cholesterol level is less than 175? Use a TI-83 to find the probability. There is a 5. 48% that a man will have a cholesterol level less than 175 mpd. A man from the US is selected at random. What is the probability that his cholesterol is between 190 and 225? There is a 49. 68% chance that a man will have a cholesterol level between 190 and 225 mpd.

TOTD The time per week a student uses a lab computer is normally distributed, with a mean of 6. 2 hours and a standard deviation of 0. 9 hour. A student is randomly selected. Find the probability that the student uses a lab computer less than 4 hours per week. Find the probability that the student uses a lab computer between 4 and 7 hours per week. Find the probability that the student uses a lab computer more than 7 hours per week.