Topic 6 Day 2

The following table shows the probability distribution for the number of books a student typically buys at the annual book fair held at an elementary school. Let the random variable B represent the number of books a student buys at the next book fair. What is the expected value of B?

• 0

• 1.00

• 1.79

• 3.50

• 28

At a certain bakery, the price of each doughnut is $1.50. Let the random variable D represent the number of doughnuts a typical customer purchases each day. The expected value and variance of the probability distribution of D are 2.6 doughnuts and 3.6 (doughnuts)², respectively. Let the random variable P represent the price of the doughnuts that a typical customer purchases each day. Which of the following is the standard deviation, in dollars, of the probability distribution of P?

• 1.5(3.6)

• 1.5√3.6

• √1.5(3.6)

• 1.5(2.6)

• 1.5√2.6

The quality control manager at a factory records the number of equipment breakdowns each day. Let the random variable Y represent the number of breakdowns in one day. The standard deviation of Y is 0.28. Which of the following is the best interpretation of the standard deviation?

• (a)

• (b)

• (c)

• (d)

• (e)

Data were collected on the number of days per week that members visit a certain fitness center. The values varied from 0 to 7, and a distribution of relative frequencies for the values was created. Let the random variable X represent the number of days per week that a member visits. The mean of X is 3.12. Which of the following statements is the best interpretation of the mean?

• Each member visits the fitness center 3 or 4 days per week.

• The average number of days that each member visits the fitness center is 3.12 days per week.

• Half the members visit the fitness center 3 days per week or less, and the other half visit 4 days per week or more.

• The long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

• For a random sample of members selected from the population, the average number of visits for the sample will be 3.12 days per week.

Let the random variable Q represent the number of students who go to a certain teacher's office hour each day. The standard deviation of Q is 2.2. Which of the following is the best interpretation of the standard deviation?

• a

• b

• c

• d

• e

For a certain dog breed, the number of puppies in a litter typically varies from 2 to 6. The following table shows the probability distribution of the random variable N, where N represents the number of puppies in a litter. Also shown are the squared deviations, or distances, from the expected value of 4.5 for the distribution. What is the variance of the distribution?

• 1.12

• 1.25

• 1.41

• 1.58

• 2.25