Cumulative Exam — Cumulative exam Answers

Response time is an important statistic for measuring the effectiveness of a fire department, and is measured as the difference between the time a fire station receives a call and the time the first piece of fire equipment leaves the station. The response times for fire departments in a large city are found to have an approximately Normal distribution, with a mean of 4.5 minutes and a standard deviation of 1.2 minutes. What percentage of fire station response times are under 3 minutes?Find the z-table here.

A school district wanted to compare ACT scores between two of its schools (school A and school B). The dotplots below summarize the ACT scores for simple random samples of 30 students from each school.

An experiment is proposed to measure the effectiveness of a brand of sunscreen. Adult volunteers are randomly assigned to one of two brands of sunscreen and asked to enjoy a normal day at the beach. Each volunteer is asked to report back to the administrators after two hours, at which time both arms are assessed for sun exposure.

A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers put an ad online asking for volunteers to participate in the study. One hundred subjects replied and were informed that one group would receive the new cream and the other would receive a cream with no active ingredient. All 100 subjects were exposed to poison ivy. Fifty were then assigned to the group with the new cream, and 50 were assigned to the group with the cream with no active ingredient. After three days, technicians recorded the subjects’ level of irritation.

A botanist wants to determine if a fertilizer is effective in the growth of plants. He randomly selects 100 of the same type of seedling and randomly assigns them to two groups: one that uses the fertilizer, and one that does not. He makes sure the plants all have the same amount of water, soil, and light for two months. At the end of two months, he measures the heights of the plants and finds that the ones receiving the fertilizer are significantly taller.

A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation ŷ = 4.9x + 15.2, where x represents the attendance (in thousands) and ŷ is the predicted number of wins. What is the predicted number of wins for a team that has an attendance of 17,000?

The parallel boxplots below display the bag weights of two different brands, A and B, of granola.Which statement best compares the variability of the distributions for the bag weights?

The box plots show the distributions of weights of cucumbers and zucchini collected from a garden. Which statement explains the best measure of variability to use to compare the data sets?

An urban planner collects data on how park trails are used by residents. The planner looks at two trails: one that winds through an urban area and another in a suburban park. The table shows the number of users who walk, jog, or bike the trail. Activity WalkJogBikeTotalType of ParkUrban765823157Suburban1257642243 Total20113465400What proportion of suburban park users bike on the park trail?

The stemplot below displays the times, in seconds, for 25 students to run 100 meters.