# Mathematics

Q1. Which of the following is true regarding the sampling distribution of the mean for a large sample size?

a. It has the same shape, mean, and standard deviation as the population.

b. It has a normal distribution with the same mean and standard deviation as the population.

c. It has the same shape and mean as the population, but has a smaller standard deviation.

d. It has a normal distribution with the same mean as the population but with a smaller standard deviation.

Q2. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that annual household income is over $25,000 if the residents of a household do not own 2 cars is:

a. 0.12

b. 0.18

c. 0.40

d. 0.55

Q3. The collection and summarization of the socioeconomic and physical characteristics of the employees of a particular firm is an example of:

a. inferential statistics.

b. descriptive statistics.

c. a parameter.

d. a statistic.

Q4. The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day.

If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant to use 25 days of data to construct the interval estimate, what confidence level can she attach to the interval estimate?

a. 99.7%

b. 99.0%

c. 98.0%

d. 95.4%

Q5. Referring to the histogram, how many graduating seniors attended the luncheon?

a. 4

b. 152

c. 275

d. 388

Q6. The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.

Time (in Minutes) | Relative Frequency |

0 but less than 5 | 0.37 |

5 but less than 10 | 0.22 |

10 but less than 15 | 0.15 |

15 but less than 20 | 0.10 |

20 but less than 25 | 0.07 |

25 but less than 30 | 0.07 |

30 or more | 0.02 |

Referring to the table, if 10 calls lasted 30 minutes or more, how many calls lasted less than 5 minutes?

a. 10

b. 185

c. 295

d. 500

Q7. The collection of all possible events is called:

a. a simple probability.

b. a sample space.

c. a joint probability.

d. the null set.

Q8. A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the following distribution:

Price: | $10.00 | $12.50 | $15.00 |

Probability: | 0.35 | 0.40 | 0.25 |

How much should the lab budget for next year’s rat orders be, assuming this distribution does not change?

a. $520

b. $637

c. $650

d. $780

Q9. A professor of economics at a small Texas university wanted to determine what year in school students were taking his tough economics course. Shown below is a pie chart of the results. What percentage of the class took the course prior to reaching their senior year?

a. 14%

b. 44%

c. 54%

d. 86%

Q10. Since a _______ is not a randomly selected probability sample, there is no way to know how well it represents the overall population.

a. simple random sample

b. quota sample

c. stratified sample

d. cluster sample

Q11. A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the population from which the study was sampled.

a. The 250 randomly selected adult American pine trees in the forest.

b. The 25,000 adult American pine trees in the forest.

c. All the adult American pine trees taller than 60 feet in the world.

d. All American pine trees, of any age, in the forest.

Q12. A population frame for a survey contains a listing of 72,345 names. Using a table of random numbers, how many digits will the code numbers for each member of your population contain?

a. 3

b. 4

c. 5

d. 6

Q13. The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the portion of students at her university who visited campus bars every weekend. Her advisor took a random sample of 250 students. The portion of students in the sample who visited campus bars every weekend is an example of a __________.

a. categorical random variable

b. discrete random variable

c. parameter

d. statistic

Q14. The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.

Time (in Minutes) | Relative Frequency |

0 but less than 5 | 0.37 |

5 but less than 10 | 0.22 |

10 but less than 15 | 0.15 |

15 but less than 20 | 0.10 |

20 but less than 25 | 0.07 |

25 but less than 30 | 0.07 |

30 or more | 0.02 |

Referring to Table 2-5, if 100 calls were randomly sampled, how many calls lasted 15 minutes or longer?

a. 10

b. 14

c. 26

d. 74

Q15. If two events are mutually exclusive, what is the probability that one or the other occurs?

a. 0

b. 0.50

c. 1.00

d. Cannot be determined from the information given.

Q16. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household do not own 2 cars and have an income over $25,000 a year is:

a. 0.12

b. 0.18

c. 0.22

d. 0.48

Q17. If two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs?

a. 0.

b. 0.50.

c. 1.00.

d. Cannot be determined from the information given.

Q18. Why is the Central Limit Theorem so important to the study of sampling distributions?

a. It allows us to disregard the size of the sample selected when the population is not normal.

b. It allows us to disregard the shape of the sampling distribution when the size of the population is large.

c. It allows us to disregard the size of the population we are sampling from.

d. It allows us to disregard the shape of the population whennis large.