Normal Distributions

A grading scale is set up for 1000 students’ test scores. It is assumed that the scores are normally distributed with a mean score of 75 and a standard deviation of 15. Calculate the score that lies -2 standard deviation from the mean.

• 60

• 475

• 45

• 9500

What percent of a normal distribution lies outside of ±3 standard deviations?

• 99.7%

• .15%

• .3%

• 100%

In an Oreo factory, the mean mass of a cookie is given as 40 g. For quality control, the standard deviation is 2 g. If 10 000 cookies were produced, how many cookies are within 2 g of the mean?

• 6800

• 9500

• 3200

• 9750

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. About what percent of the products last between 12 and 15 days?

• 68%

• 99.7%

• 95%

• 34%

The speeds of cars on the highway have a mean of 95 km/h with a standard deviation of 5 km/h. What percentage of cars averaged less than 85 km/h?

• .15%

• 2.35%

• 2.5%

• 18.5%

The mean life of a tire is 30 000 km. The standard deviation is 2000 km. 68% of all tires will have a life between ______km and ______km.

• 26000 and 34000

• 28000 and 32000

• 24000 and 34000

• 22000 and 36000

The Floppy Disk Company makes 3.5 inch floppy disks (mean) for disk drives that are 3.7 inches wide. The size of a manufactures disk is normally distributed with a standard deviation of 0.1 inches. The company manufactures 1000 disks every hour. In one hour, how many disks would you expect to be between 3.4 inches and 3.7 inches?

• 34

• 135

• 68

• 815

The distribution above is normal. What percent lies below the curve?

• 68%

• 95%

• 99.7%

• 100%

The distribution above is normal. What percent lies between ±3 standard deviations?

• 68%

• 95%

• 99.7%

• .3%

Between what two standard deviations of a normal distribution contain 68% of the data?

• one below and one above
• two below and two above
• two below and zero
• zero and two above