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

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CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.4

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

• 99.7%

• .15%

• .3%

• 100%

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CCSS.HSS.ID.A.4

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

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CCSS.HSS.ID.A.4

Suppose the heights of adult men are normally distributed. The heights of a sample of 30 men are shown below in inches.

65, 83, 69, 67, 69, 67, 67, 72, 85, 68, 73, 65, 67, 65, 72, 71, 67, 73, 68, 72, 61, 75, 66, 78, 65, 71, 68, 76, 67, 68

Compute the standard deviation of the sample.

• 5.31

• 70

• 5.23

• 68

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CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.4

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%

Tags

CCSS.HSS.ID.A.4

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%

Tags

CCSS.HSS.ID.A.4

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

Tags

CCSS.HSS.ID.A.4

A bottle of fruit punch contains at least 473 ml. The machine that fills the bottles is set so that the mean volume is 477 ml. The volumes in the bottles are normally distributed. The standard deviation is 2 ml. Would a bottle that ea filled to 470 ml be an outlier?

• Yes

• No

• Beat Rayburn

• BHI

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CCSS.HSS.ID.A.3

CCSS.HSS.ID.A.4

A sampling distribution for means has a mean of 18 and a standard deviation of 3.0 when the sample size is n = 49. Calculate the standard error?

• 3/49

• 3/7

• 1/6

• 6

Suppose the heights of adult men are normally distributed. The heights of a sample of 30 men are shown below in inches.

65, 83, 69, 67, 69, 67, 67, 72, 85, 68, 73, 65, 67, 65, 72, 71, 67, 73, 68, 72, 61, 75, 66, 78, 65, 71, 68, 76, 67, 68

Compute the mean of the sample.

• 71

• 70

• 69

• 68

Tags

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.4