Normal Distributions and Outlier Calculation Review

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

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

• 0.1762

• 0.8238

• -0.93

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 more than 7 accidents?

• 0.3446

• 0.2856

• 0.4

• 0.6554

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

The heights of male students are Normally distributed with mean 1.7 m and standard deviation 0.2 m

In a population of 400 male students, how many would you expect to have a height between 1.4 m and 1.6 m?

• 24

• 54

• 97

• 100

A data set has a normal distribution with a mean of 4800 grams and a standard deviation of 200 grams. A value from the data set is randomly chosen. What is the probability that the value is 5140 grams or less? Use the standard normal table.

Mathematical Equivalence

ON

The ages of the population of people living in Meru area in Ipoh are Normally distributed with mean 43 and standard deviation 14

The town has a population of 5,000.

How many would you expect to be aged between 22 and 57?

You can use this Standard Normal Distribution curve:

• 1750

• 3860

• 3870

• 4330

The weights of chocolate truffles made by a candy shop are approximately normally distributed with a mean of 2 ounces and a standard deviation of 0.3 ounce. What is the probability that a randomly selected chocolate truffle from this candy shop will weigh less than 1.5 ounces? The candy shop assembles gift boxes that contain 8 randomly selected chocolate truffles. What is the probability that none of the truffles in a gift box weighs less than 1.5 ounces? The weights of gift boxes, including all packaging materials, are approximately normally distributed with a mean of 3 ounces and a standard deviation of 0.5 ounce. If 8 randomly selected chocolate truffles are placed into a randomly selected gift box, describe the distribution of the total weight of the gift box and truffles.

Which data point did the statistician exclude?

• (2.3, 11.0)

• (4.2, 16.5)

• (6.4, 23.1)

• (8.2, 24.3)

The D.O.T. collected data for a particular stretch of I-85 and found that the average speed was 70mph with a standard deviation of 15mph with a normal distribution. The actual speed limit for the stretch of road is a maximum of 70mph and a minimum of 40mph. What percentage of drivers actually drive between 40mph and 70mph?

• 34%

• 47.5%

• 68%

• 95%