**12.7 Normal Distributions**

Idleness is not doing nothing. Idleness is being free to do anything.

**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) 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.

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?

**12.7 Normal Distributions**

**HW: 9 – 27 odd**

Idleness is not doing nothing. Idleness is being free to do anything.