Statistics Review Normal Distribution

This data is normally distributed.  What percent of the data is in the shaded region?

• 68%

• 95%

• 99.7%

• 50%

What percent of people within 1 standard deviation of the mean?

• 99.7

• 34

• 68

• 95

Identify the mean and standard deviation for this normal distribution.

• The mean is 100 and the standard deviation is 15.

• The mean is 100 and the standard deviation is 30.

• The mean is 15 and the standard deviation is 100.

• The mean is 30 and the standard deviation is 100.

A real estate agent, working entirely on commission, makes a weekly average of $850 with a standard deviation of $260 selling property in the city, and an average of $1340 with a standard deviation of $390 selling property in the suburbs. Assuming independence, what are the mean and standard deviation of her total weekly sales?

• μX = 1095, σX = 325

• μX = 1095, σX = 469

• μX = 2190, σX = 325

• μX = 2190, σX = 469

Which of these variables is least likely to have a normal distribution?

• Ages of 2000 students at a local high school.

• Weights of 200 of the same candy bar in a shipment to a local supermarket.

• Heights of 100 white pine trees in a forest.

• Amount of soda in 60 cups filled by an automated machine at a fast-food restaurant.

The grades on a quiz in statistics had an average of 73 with a standard deviation of 5. The teacher decided to curve the quiz grades using the equation: curve = 1.3(grade) - 10. What are the mean and standard deviation of the curved grades?

• μ = 94.9, σ = 6.5

• μ = 84.9, σ = 6.5

• μ = 84.9, σ = -3.5

• μ = 84.9, σ = 5

The 35th percentile of a population is the number x such that:

• 35% of the population scores are above x.

• 65% of the population scores are above x.

• x is 65% of the population mean.

• x is 35% of the population mean.

A company wants to make a new snack mix. They decide to mix popcorn and M&M’s. Weights of bags of M&M’s have a mean of 8.2 ounces with standard deviation of 0.2 ounces. Weights of bags of popcorn have a mean of 3.5 ounces with a standard deviation of 1.8 ounces. What is the expected combined mean and standard deviation when the bags are mixed?

• Mean: 11.7 ounces, Standard Deviation: 1.811 ounces

• Mean: 11.7 ounces, Standard Deviation: 1.8 ounces

• Mean: 11.7 ounces, Standard Deviation: 2.2 ounces

• Mean: 11.7 ounces, Standard Deviation: 2.6 ounces

A study of elite distance runners found a mean body weight of 60 kilograms (kg), with a standard deviation of 6 kg. Assuming that the distribution of weights is approximately normal. Use the 68–95–99.7 rule to find the percentage of runners whose body weight is between 54 and 72 kg.

• 81.5%

• 95%

• 99.7%

• 34%

A study of elite distance runners found a mean body weight of 60 kilograms (kg), with a standard deviation of 6 kg. Assuming that the distribution of weights is approximately normal. What percentage of runners have body weights above 72 kg?

• 10%

• 25%

• 2.5%

• 75%