1. The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.3 miles per gallon. a. That is the probability that a randomly selected hybrid gets more than 61 miles per gallon? b. What is the probability that a randomly selected hybrid gets 51 miles per gallon or less? c. What is the probability that a randomly selected hybrid gets between 57 and 62 miles per gallon? d. What is the probability that a randomly selected hybrid gets less than 46 miles per gallon?
2. Suppose a geyser has a mean time between eruptions of 94 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 35 minutes, answer the following questions.
(a) What is the probability that a randomly selected time interval between eruptions is longer than 108 minutes?
(b) What is the probability that a random sample of 17 time intervals between eruptions has a mean longer than 108 minutes?
(c) What is the probability that a random sample of 41 time intervals between eruptions has a mean longer than 108 minutes?
(d) What effect does increasing the sample size have on the probability? Provide an explanation for this result. Choose the correct answer below.
- The probability increases because the variability in the sample mean increases as the sample size increases.
- The probability increases because the variability in the sample mean decreases as the sample size increases.
- The probability decreases because the variability in the sample mean decreases as the sample size increases.
- The probability decreases because the variability in the sample mean increases as the sample size increases.
(e) What might you conclude if a random sample of 41 time intervals between eruptions has a mean longer than 108 minutes? Choose the best answer below.
- The population mean must be less than 94, since the probability is so low.
- The population mean may be greater than 94.
- The population mean is 94 minutes, and this is an example of a typical sampling.
- The population mean cannot be 94, since the probability is so low.