Download 5.2 Normal Distributions Finding Probabilities

Statistics
5.2 Normal Distributions: Finding Probabilities
Objectives: Probability and Normal Distributions
Procedure:
1. Probability and Normal Distributions:
a. Example 1: Finding probabilities for normal distributions:
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.
b. Example 2: Finding probabilities for normal distributions:
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.
c. Example 3: Finding probabilities for normal distributions:
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
More than 39 minutes
Between 33 and 60 minutes
d. Example 4: Using technology to find normal probabilities:
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.
A man from the US is selected at random. What is the probability that his
cholesterol is between 190 and 225?
2. HW: p. 232 (3 – 24 mo3)