The Normal Distribution Practice

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

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 proportion of golfers that are between 30 and 46 years old.

• 68%

• 94%

• 95%

• 99.7%

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%

Which interval shows 95% of the data given a mean of 15 and a standard deviation of 3? 

• 9 to 21
• 12 to 18
• 6 to 24
• 13 to 16

Which interval shows 99.7% of the data given a mean of 15 and a standard deviation of 3? 

• 9 to 21
• 12 to 18
• 6 to 24
• 13 to 16

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 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 integer level of IQ qualifies one to be a member of Mensa?

• 130
• 131
• 145
• 120

A manufacturer contracts to supply ball bearings with diameters between 24.60mm and 25.4mm. Product analysis indicates that the ball bearings manufactured have diameters that are normally distributed with a mean of 25.10mm and a standard deviation of .20mm. What percentage of ball bearings fail to satisfy the contract specifications?

• 92.7%
• 7.3%
• 48.2%
• 33.2%

The average number of calories in a 1.5-ounce chocolate bar is 225.  Suppose that the distribution of calories is approximately normal with a σ of 10.  Find the probability that a randomly selected chocolate bar will have between 200 and 220 calories. 

• 0.9876
• 0.3023
• 0.0098
• 0.3320