Normal Distributions Application

68% of the marks in a test are between 51 and 64

Assuming this data is normally distributed, what are the mean and standard deviation?

• Mean = 57

  S.D. = 6.5

• Mean = 57

  S.D. = 7

• Mean = 57.5

  S.D. = 6.5

• Mean = 57.5

  S.D. = 13

Company pack coffee in bags marked as 250 g

A large number of packs of coffee were weighed and the mean and standard deviation were calculated as 255 g and 2.5 g respectively.

Assuming this data is normally distributed, what percentage of packs are underweight?

• 2.5%

• 3.5%

• 4%

• 5%

Students pass a test if they score 50% or more. The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively. Assuming this data is normally distributed, what percentage of students pass the test? in percentage...

• 5

• 16

• 24

• 32

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 4.6 seconds?

• 0.83

• 1.07

• -2

• -1.07

According to the empirical rule, how much of the data falls within 3 standard deviations? 

• 25%

• 68%

• 95%

• 99.7%

Use the following information and the Empirical Rule to estimate the answer.

The ages of golfers are normally distributed, with a mean of 38 and a standard deviation of 4.

Find the percentage of golfers that are between 30 and 46 years old.

• 68%

• 94%

• 95%

• 99.7%

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score between 68 and 82

• 11

• 2

• 340

• 498

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score higher than 68?

• 11

• 12

• 420

• 250

The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. What percent of men are between 64 and 66.5 inches tall? 

• 50%

• 2.5%

• 13.5%

• 34%

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 2.3 and 3.5?

• 68%

• 99.7%

• 95%

• 84%