STAT 4.7-9

Let random variable U represent the field goal percentage (percentage of shots made) for players in a basketball league. The following table shows the probability distribution of the random variable U.

Fatima claims that the distribution of U is uniform with a median of 0.4 field goal percentage. Is Fatima’s claim supported by the table?

• Yes, the distribution is uniform with a median of 0.4 field goal percentage.

• No, the distribution is uniform with a median of 0.5 field goal percentage.

• No, the distribution is skewed to the right with a median of 0.4 field goal percentage.

• No, the distribution is skewed to the right with a median of 0.5 field goal percentage.

• No, the distribution is skewed to the left with a median of 0.4 field goal percentage.

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

• 28.0

At a large regional collegiate women’s swim meet, an official records the time it takes each swimmer to swim 100 meters for all swimmers who compete in only one stroke category. The following table shows the mean times and corresponding standard deviations for the collegiate women at the swim meet for each of the four stroke categories.

For each of the 4 stroke categories, consider a random variable representing the time of a randomly selected swimmer in that category. What is the standard deviation of the sum of the 4 random variables?

• 0.83s

• 1.67s

• 2.80s

• 3.32s

• 3.76s

A player pays $15 to play a game in which a chip is randomly selected from a bag of chips. The bag contains 10 red chips, 4 blue chips, and 6 yellow chips. The player wins $5 if a red chip is selected, $10 if a blue chip is selected, and $20 if a yellow chip is selected. Let the random variable X represent the amount won from the selection of the chip, and let the random variable W represent the total amount won, where W=X−15. What is the mean of W ?

• $10.50

• $4.50

• -$4.50

• -$6.50

• -$10.50

The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S has mean 7 and standard deviation 3. If R and S are independent, what are the mean and standard deviation of the distribution of R−S ?

• Mean 3 and standard deviation 1

• Mean 3 and standard deviation 5

• Mean 3 and standard deviation 7

• Mean 17 and standard deviation 1

• Mean 17 and standard deviation 5

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 ?

• 
• 
• 
• 
• 

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?

• The number of breakdowns on a randomly selected day is expected to be 0.28.

• The number of breakdowns on a randomly selected day will be 0.28 away from the mean.

• The average number of breakdowns per day for a random sample of days is expected to be 0.28.

• On average, the number of breakdowns per day varies from the mean by about 0.28.

• The number of breakdowns per day for a random sample of days is expected to be 0.28 away from the mean.

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 random variable Y represent the number of interviews conducted for job openings at a certain company. The following table shows the cumulative probability distribution of the discrete random variable Y.

Khaleed claims that the distribution of Y is skewed to the left with mean equal to 8 interviews. Is Khaleed’s claim correct?

• Yes, the distribution is skewed to the left with mean equal to 8 interviews

• No, the distribution is skewed to the left with mean greater than 8 interviews.

• No, the distribution is skewed to the right with mean equal to 8 interviews.

• No, the distribution is uniform with mean equal to 8 interviews.

• No, the distribution is uniform with mean greater than 8 interviews.

At a certain company, loan agents are paid based on the number of loans they close in a day. Based on company records, the number of loans X that a randomly selected loan agent closes on a randomly selected day has the probability distribution below.

At the company, the daily salary of a loan agent is $150 plus $50 per loan closed. Let Y represent the amount of money made by a randomly selected loan agent on a randomly selected day. Which of the following statements is NOT true?

• The mean of X is less than the mean of Y

• The standard deviation of Y is approximately $71.

• The mean daily salary is greater than $350 per day.

• The standard deviation of X is less than the standard deviation of Y.

• The shape of the probability distribution of Y is unimodal and roughly symmetric.