The Bell Curve
Normal Distribution – shows data that vary randomly from the mean.
Normal Curve – The pattern the data form is a bell-shaped curve.
The Standard Normal Bell Curve
68% of the data fall within one standard deviation of the mean
95% of the data fall within two standard deviations of the mean
Using the Standard Normal Curve
Ex 1) A survey of the employees of XYZ Corporation found that the
mean of the morning commute times to work was 18 minutes. The
standard deviation was 4 minutes. Sketch a normal curve showing the
commute times at one, two, and three standard deviations from the mean.
1) What values are one standard
deviation from the mean?
2) What percent of the data can you
expect to find between 18 and 22
minutes?
3) Of 124 commuters, how many could
you expect to be driving between 22
and 25 minutes to work?
Using the Standard Normal Curve
Ex 2) The jaw widths of a population of great white
sharks are normally distributed abut a mean of 15.7 in.
The standard deviation of the widths is 2.8 in. Sketch a
normal curve showing the jaw widths at one, two, and
three standard deviations from the mean.
Using the Standard Normal Curve
Ex 3) In a survey of 240 people, the responses to the
question, “How much time do you spend in the shower
every day?” were normally distributed. The mean was
15 minutes; the standard deviation was 2 minutes.
Sketch a normal curve showing the shower times within
one, two, and three standard deviations of the mean.
1) What percentage of people’s shower time is within two standard
deviations of the mean?
2) How many people shower between 17 and 19 minutes?
3) How many people shower less than 13 minutes and greater than 17
minutes?
Using the Standard Normal Curve
Ex 4) In a university lecture class with 174 students, the
final exam scores have a mean of 68.5 and a standard
deviation of 7.3. The grades on the exams follow a
normal curve
1) About how many students receive grades from one to two standard
deviations above the mean?
2) About how many students receive grades of 61 or below?
Using the Standard Normal Curve
Ex 5) The number of paper clips in a truckload of boxes
are normally distributed, with a mean of 100 and a
standard deviation of 5.
1) What percentage of the boxes contain less than 95 paper clips?
2) About how many boxes have between 100 and 110 paper clips?
12.7 Normal Distributions
Homework #31
Pg 695 #5-13