11-9 Normal Distributions

Quick Review

A discrete probability distribution has a finite number of possible values, while the values for a continuous probability distribution are all the values on some interval of real numbers. A normal distribution shows data that vary from the mean in a random, continuous manner. The pattern they form is a bell-shaped curve called a normal curve. When a data set follows the normal curve, about 68% of the data fall within one standard deviation of the mean, about 95% fall within two standard deviations, and about 99.7% fall within three standard deviations.

Example

Sketch a curve for a normal distribution with mean 10 and standard deviation 4. Label the x-axis at one, two, and three standard deviations from the mean.

Exercises

For each of the following, state whether the probability distribution would be discrete or continuous.

56. distance from an arrow's impact point to the center of the bullseye
57. shoe sizes on a softball team
58. price of a gallon of premium unleaded gasoline at a randomly selected gas station
59. time a customer spends on hold during a call to a computer manufacturer's tech support
60. Auto Maintenance Suppose the time required for an auto shop to do a tune-up is normally distributed, with a mean of 102 minutes and a standard deviation of 18 minutes. What is the probability that a tune-up will take more than two hours? Under 66 minutes?

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