U1T4 Review Normal Distribution

The distribution of the scores on the last test is normally distributed with a mean of 82, and approximately 68% of the scores are between 77 and 87. What is the approximate standard deviation of the scores?

• 2

• 3

• 4

• 5

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 heights of American men aged 18 to 24 are approximately normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. About what percentage of the men are over 70.5 inches tall?

• 2.5%

• 84%

• 16%

• 97.5%

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.

If your score on a test is at the 60th percentile, where do you know that your score lies?

• below the first quartile.

• between the first quartile and the median.

• between the median and the third quartile.

• above the third quartile.

Jack and Jill are both enthusiastic players of a certain computer game. Over the past year, Jack’s mean score when playing the game is 12,400 with a standard deviation of 1500. During the same period, Jill’s mean score is 14,200, with a standard deviation of 2000. They devise a fair contest: each one will play the game once, and they will compare z-scores. Jack gets a score of 14,000, and Jill gets a score of 16,000. What were each of their z-scores?

• Jack: 1.07, Jill: 0.95

• Jack: 1.067, Jill: 0.90

• Jack: 1.07, Jill: 0.91

• Jack: 1.33, Jill: 0.98

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. a) 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%