PFA
1. The United States Forest Service is interested in determining the percentage of acreage in Yosemite that would fall below a certain threshold of trees per acre so that they might estimate how many new trees to buy in order to make sure all of Yosemite is considered well-forested. The distribution of trees per acre in Yosemite is approximately Normal with a mean of 45 trees per acre and a standard deviation of 3 trees per acre. A tree per acre count below 39 is considered understocked for a forest. Roughly what percentage of acres in Yosemite would you say is "understocked"? a. 95% b. 0.15% c. 0.3% d. 5% e. 2.3% 7. The histogram below shows the distribution of homework grades across all STAT-303 sections. Suppose the mean of this distribution is 62, with a standard deviation of 13. What is the probability that a randomly-selected student scored higher than a 60? a. 0.44 b. The probability cannot be calculated because the distribution is not Normal; it is skewed left c. 0.5 d. 0.56 e. The probability cannot be calculated because the distribution is not Normal; it is skewed right 8. An index that is a standardized measure used in observing infants over time is approximately normal with a mean of 96 and a standard deviation of 10. What index score is greater than 33% of the population index scores? a. -0.44 b. 52.24 c. 100.40 d. 0.3707 e. 91.60 12. In 2019, 15.9% of Broadway actors were acting in their first role on Broadway. Suppose we took a survey of 38 Broadway actors and found that 18.4% of the actors we surveyed were first-timers. What are the mean and standard deviation for the sampling distribution of p^? a. Mean: 0.159, Standard Deviation: 0.063 b. Mean: 0.184, Standard Deviation: 0.059 c. Mean: 0.159, Standard Deviation: 0.059 d. Mean: 0.159, Standard Deviation: 0.3657 e. Mean: 0.184, Standard Deviation: 0.063 14. In which of the following scenarios can we assume that the sampling distribution is approximately normal? I. The population distribution for a mean is approximately normal, but the sample size is 5. II. The population distribution for a mean is not normal, but the sample size is 25. III. The population distribution for a mean is not normal, but the sample size is 50. IV. The sample size for a proportion is large enough that np and n(1-p) are both 15. V. The sample size for a proportion is large enough that np and n(1-p) are both 20. a. I, II, III, V b. III, IV, V c. I, III, V d. I, III, IV, V e. I, II, III, IV, V 15. In 2019 the CDC reported that 14.0% of US adults are smokers. Suppose you take a random sample of 30 smokers and find that the proportion of them who are current smokers is 16.7%.What is the mean and the standard deviation of the sampling distribution of p^ ? a. mean = 0.167, standard deviation = 0.063 b. mean = 0.140, standard deviation = 0.068 c. mean = 0.140, standard deviation = 0.063 d. mean = 0.167, standard deviation = 0.068 16. The National Center for Health Statistics reports that the mean systolic blood pressure for males 35 to 44 years of age is 128. A medical director wants to test whether the mean systolic blood pressure of company executives between the ages of 35 and 44 is different from that of the general population. He asks the company's statistician to give him the results of this hypothesis test, but instead he receives the 95% confidence interval of