Statistics & Normal Distributions

The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds.  What is the z-score for a player who runs a time of 5.6 seconds?

• -1.33
• 1.33
• 0.88
• 1.02

Tags

CCSS.HSS.ID.A.4

The number of accidents per week at a company is approximately normally distributed. The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5. What proportion of weeks would you expect to have less than 5 accidents?

• 0.6915

• 0.1753

• 0.8238

• -0.93

The average waist size for teenage males is 29 inches with a standard deviation of 1.4 inch. 
If waist sizes are normally distributed, estimate the proportion of teenagers who will have waist sizes greater than 31 inches?

• 92.4%
• 10.5%
• 16%
• 7.6%

Tags

CCSS.HSS.ID.A.4

The scoring of modern IQ is such that Intelligence Quotients (IQs) have a normal distribution of μ= 100 and σ = 15.

Mensa International is a non-profit organization that accepts only people with IQ score within the top 2%. What level of IQ qualifies one to be a member of Mensa?

• 115.25

• 130.81

• 145.14

• 69.19

The z-score represents.....

• the amount of standard deviations a data value is above or below the mean.
• the percentile the data value is above or below the mean.
• the amount of standard deviations a data value is above or below the median.
• the percent the data value is above or below the mean.

Tags

CCSS.HSS.ID.A.4

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.  
Suppose a male long jumper's jump ranked in the 75th percentile.  How long was his jump?

• 0.67 inch
• 263 inches
• 272.44 inches
• 277.25 inches

Tags

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.3

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%
• 34%
• 16%
• 2.5%

Tags

CCSS.HSF-LE.A.1B

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

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%

• 2.28%

• 18.15%

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