Probability. Question 2: Sampling

#1 Probability. Please provide a spreadsheet and show work.

A survey of 200 college graduates who have been working for at least 3 years found that 90 owned only mutual funds, 20 owned only stocks, and 70 owned both.

What is the probability that an individual owns a stock? A mutual fund? What is the probability that an individual owns neither stocks nor mutual funds? What is the probability that an individual owns either a stock or a mutual fund?

#2 Sampling. Please provide a spreadsheet and show work.

A study of nonfatal occupational injuries in the United States found that about 31% of all injuries in the service sector involved the back. The National Institute for Occupational Safety and Health (NIOSH) recommended conducting a comprehensive ergonomics assessment of jobs and workstations. In response to this information, Mark Glassmeyer developed a unique ergonomic handcart to help field service engineers be more productive and also to reduce back injuries from lifting parts and equipment during service calls. Using a sample of 382 field service engineers who were provided with these carts, Mark collected the following data:

                                                                                Year 1                                    Year 2

                                                                                (Without Cart)                   (With Cart)

Average call time                                             8.27 hours                           7.98 hours

Standard deviation call time                        1.36 hours                           1.21 hours

Proportion of back injuries                          0.018                                     0.010

Find 95% confidence intervals for the average call times and proportion of back injuries in each year. What conclusions would you reach based on your results?