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.