# Mathematics

Summer (June) 2017

BIA2610

Multiple Choice, Questions 1-5. Place only one letter choice in the space provided. (5 points each)

_______ 1. The human resources department at a major high tech company recently conducted an employee satisfaction survey of 50 of its 2,000 employees. Data were collected on such variables as age, gender, current salary, level of overall satisfaction on a scale from 1 to 5, job title, and county of residence. Which of the variables would be considered categorical data?

a. age, gender, job satisfaction

b. job satisfaction, job title, gender, county of residence, age

c. county of residence, gender, job title, job satisfaction

d. all variables listed are qualitative

_______ 2. Which of the following does a histogram NOT show?

a. center and shape of data

b. relationship between two variables

c. relative frequency of data

d. spread of data

_______ 3. At the end of the school term, students are asked to rate the course and instructor by indicating on a scale of 1-5 how well they liked the course. The data generated from this question are examples of:

a. interval data

b. ordinal data

c. ratio data

d. nominal data

______ 4. When the production manager selects a sample of items that have been produced on her production line and computes the proportion of those items that are defective, the proportion is referred to as a:

a. parameter

b. population

c. mean

d. statistic

_______5. General Electric Corporation tracks employee turnover annually. They currently have a data set that contains turnover rate each year for the past 20 years. What type of data do they have?

a. time series data

b. cross-sectional data

c. nominal data

d. ordinal data

Open Answer, Questions 6-9. Answer each question as completely as possible. Partial credit will be given, so show all work. **An answer without any work shown will be taken as a guess and will receive zero points. For example, if you use Excel, write down the function or formula you used. **Indicate your final answer by circling it (25 points each).

6. Given the following observations from a sample, calculate the variance and standard deviation.

199 | 150 | 267 | 58 | 112 | 109 | 43 |

## Variance

## Standard deviation

7. A study in the *Journal of the American Medical Association* (February 20, 2008) found that patients who go into cardiac arrest while in the hospital are more likely to die if it happens after 11 pm. The study investigated 58,593 cardiac arrests that occurred during the day or evening. Of those, 11,604 survived to leave the hospital. There were 28,155 cardiac arrests during the shift that began at 11 pm, commonly referred to as the graveyard shift. Of those, 4,139 survived for discharge. The following contingency table summarizes the results of the study.

(**round all answers to 3 decimal places**)

a. | What is the probability that a randomly selected patient experienced cardiac arrest during the graveyard shift? |

b. | Given that a randomly selected patient experienced cardiac arrest during the graveyard shift, what is the probability the patient survived for discharge? |

c. What is the probability that a randomly selected patient had a cardiac arrest during the day or evening shift and did not survive for discharge?

d. What is the probability that a randomly selected patient survived for discharge or had a cardiac arrest during the graveyard shift?

8. Consider the following data set:

Calculate the 20th and 87th percentiles.

20th

87th

9. Consider the following frequency distribution:

Class | Frequency | Relative frequency | Cumulative relative frequency |

1000 up to 1100 | 4 | ||

1100 up to 1200 | 8 | ||

1200 up to 1300 | 9 | ||

1300 up to 1400 | 3 |

a. Fill in the relative frequency and cumulative relative frequency values. (round your answers to 3 decimal places)

b. What percent of the observations are at least 1100 but less than 1200? (round to 1 decimal place)

c. What percent of the observations are less than 1300? (round to 1 decimal place)

10. India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too high to be sustainable. A demographer computes the following probability distribution of the household size in India.

Household Size | Probability |

1 | 0.05 |

2 | 0.09 |

3 | 0.12 |

4 | 0.24 |

5 | 0.25 |

6 | 0.25 |

a. What is the expected household size based on this probability distribution? (13 pts)

b. What is the household size standard deviation? (12 pts)

11. At a local commuter college, 60% of students who enter the college as freshmen go on to graduate. Five freshmen are randomly selected. ROUND ALL ANSWERS TO 4 DECIMAL PLACES. SHOW WORK!

a) What is the probability that none of them graduates from the local university? (7 pts)

b) What is the probability that at most four will graduate from the local university? (9 pts)

c) What is the probability that two or less will graduate from the local university? (9 pts)

12. Find the following *z* values for the standard normal variable *Z*. (8 pts each)

a) Area to the left of *z* is 0.1056. What is *z*?

b) Area between *–z* and 0 is 0.4192. What is *z*?

d) Area between 0.37 and *z* is 0.3121. What is *z*?

13. Find the following probabilities based on a standard normal variable Z. (8 pts each)

a) P(*Z* > 0.72)

b) P(*Z *≤ -1.87)

c) P(-0.90 ≤ *Z* ≤ 2.93)

14. Americans are increasingly skimping on their sleep (National Geographic News, February 24, 2005). A health expert believes that American adults sleep an average of 6.2 hours on weekdays with a standard deviation of 1.2 hours. Assume sleep time is normally distributed.

a) What **percent** of American adults sleep more than 8 hours on weekdays? (9 pts)

b) What **percent** of American adults sleep between 4 and 8 hours on weekdays? (9 pts)

c) What is the minimum amount of sleep needed to be in the top 5%? (9 pts)