Download Normal Distribution

Homework Questions
Normal Distributions
Normal Curve
 Sometimes called the “Bell Curve”
 Used to predict outcomes of many types
of events (probabilities that things will
happen)
Properties of the Normal Curve
 Bell-shaped
 Symmetric
 X-axis is a horizontal asymptote
 Area under the curve = 1
 Maximum value occurs at the mean
 Because it is symmetric, the mean, median, and mode
all have the same value…called the center.
 Greek letter  is used to represent the mean
  is used for standard deviation
Example 1

A paper in Animal Behavior gives 11 sample distances, in
cm, which a bat can first detect a nearby insect. Assume
the population is normally distributed.
62, 23, 27, 56, 52, 34, 42, 40, 68, 45, 83
a) Compute the mean and standard deviation.
b) Draw a normal curve for this distribution.
The Empirical Rule
The Empirical Rule
 68% of the data are within one standard
deviation of the mean
 95% of the data are within two standard
deviations of the mean
 99.7% of the data are within three
standard deviations of the mean
Example 2
 A pair of running shoes lasts on average 450
miles, with a standard deviation of 50 miles. Use
the empirical rule to find the probability that a
new pair of running shoes will have the following
lifespans.
1.
2.
Between 400-500 miles
More than 550 miles
Example 3
 A survey of 1000 U.S. gas stations found that the price
charged for a gallon of regular gas can be closely
approximated by a normal distribution with a mean of $1.90
and a standard deviation of $0.20. How many of the stations
charge
a. between $1.50 and $2.30 for a gallon of regular gas?
b. less than $2.10 for a gallon of regular gas?
c. more than $2.30 for a gallon of regular gas?
Example 4
 A vegetable distributor knows that during the month of
August, the weights of its tomatoes were normally
distributed with a mean of 0.61 pound and a standard
deviation of 0.15 pound.
a. What percent of the tomatoes weighed less than 0.76
pound?
b. In a shipment of 6000 tomatoes, how many tomatoes can
be expected to weigh more than 0.31 pound?
c. In a shipment of 4500 tomatoes, how many tomatoes can
be expected to weigh between 0.31 and 0.91 pound?
Answer to #4
Homework
 13.5 worksheet