7.7 Warm Up 01.16.25

A recent report indicated that 90 percent of adults in a certain region actively try to include vegetables in their diet. A simulation was conducted that consisted of 50 trials with a population parameter of 0.9. Each trial consisted of a sample size of 10. The number of successes out of 10 was recorded, where success represented an adult trying to include vegetables in the diet. Five possible simulation results are shown. Which simulation is the best match to the one described?

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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.

A store owner reports that the probability that a customer who purchases a lawn mower will also purchase an extended warranty is 0.68. Which of the following is the best interpretation of the probability 0.68?

• For all customers who purchase a lawn mower, 68% will also purchase an extended warranty.

• For all customers of the store, 68% will purchase a lawn mower.

• For all customers who purchase an extended warranty, 68% will use the warranty.

• From the next 25 customers, 17 will purchase an extended warranty.

• From the next 25 customers, 17 will purchase a lawn mower.

Shalise competed in a jigsaw puzzle competition where participants are timed on how long they take to complete puzzles of various sizes. Shalise completed a small puzzle in 75 minutes and a large jigsaw puzzle in 140 minutes. For all participants, the distribution of completion time for the small puzzle was approximately normal with mean 60 minutes and standard deviation 15 minutes. The distribution of completion time for the large puzzle was approximately normal with mean 180 minutes and standard deviation 40 minutes. Approximately what percent of the participants had finishing times greater than Shalise’s for each puzzle?

• 16% on the small puzzle and 16% on the large puzzle

• 16% on the small puzzle and 84% on the large puzzle

• 32% on the small puzzle and 68% on the large puzzle

• 84% on the small puzzle and 84% on the large puzzle

• 84% on the small puzzle and 16% on the large puzzle

Researchers are investigating the effect of pH level in water on the breeding habits of the moon jellyfish. As part of a laboratory experiment, they will randomly assign one of three treatments, low pH, medium pH, or high pH, to the water in the tanks that hold the jellyfish. Which of the following is the best reason for the random assignment of a treatment level to an experimental unit?

• Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects.

• Randomization will make up for improper experimental design, data collection, and analysis.

• Randomization makes the analysis easier since the data can be entered into the computer in any order.

• Randomization is required by statistical consultants before they will analyze the experiment.

• Randomization means that the experiment would not need to be replicated.