my statistics exam 2

1) X ∼ N(15,5) X ∼ N (15,5), what is the P( X>1 1) P ( X > 11)? 0.7881 If X ∼ N(15,5) X ∼ N (15,5), what is the P(X<11) P ( X <11)? 0.2119 2) Suppose it is known that 10% of adolescent females in the United States have iron deficiency. In a random sample of 35 adolescent females, what is the probability that exactly 3 have iron deficiency? 84 3) A Gallup poll asked the question “If you won 10 million dollars in the lottery would you continue to work, or would you stop working?” Of the 30 randomly selected employed adults in the study, 59% said they would continue working. 90% confidence level (0.442, 0.738) 4) Construct a 95% confidence interval for the proportion of employed adults who would continue to work if they won 10 million dollars in the lottery. (0.414, 0.766) 5) An online retailer claims 90% of all orders are shipped within 12 hours of being received. Let p^ p ^be the sample proportion of orders that are shipped within 12 hours in a SRS of orders. Suppose we set our sample size to n=120 n =120 What is the probability of selecting an SRS in which less than 105 orders were shipped within 12 hours? 0.1807 An online retailer claims 90% of all orders are shipped within 12 hours of being received. Let p^ p ^ be the sample proportion of orders that are shipped within 12 hours in a SRS of orders. In a sample of size n=200 n =200, which value would be the first quartile of all sample proportions 0.8857 6) The mean amount of money spent on health insurance per month by US citizens is strongly right skewed with a mean of $456 and standard deviation of $53. Suppose a SRS of 50 US citizens is taken. Find the probability that the sample mean amount of money spent on health insurance is less than $430/month. 0.0003 7) with larger sample sizes there is a greater likelihood that the data distribution... Will look similar to the population distribution. 8) The time that it takes a randomly selected rat of a certain subspecies to find its way through a maze is normally distributed with mean μ=1.5 μ =1.5 minutes and σ=0.35 σ =0.35 minutes. Suppose 4 rats are selected. What is the probability that the sample mean time to navigate the maze is more than 1.92 minutes? 0.0082 9) An insurance company knows that in the entire population of millions of insured workers, the distribution of annual cost of workers’ compensation claims is right skewed with a mean $439 per insured worked and standard deviation $20,000. Suppose a sample of 20 workers’ compensation claim costs is taken. What is the probability that the sample mean cost is greater than $1500? This probability cannot be calculated because we do not know the sampling distribution of xˉ 10) Viral hepatitis occurs in 7% of patients who receive multiple blood transfusions during heart surgery. A SRS was taken of 200 heart surgery patients who had multiple blood transfusions. If appropriate, use the normal approximation to the binomial to find the probability that at least 10 contracted viral hepatitis. 0.8662 11)Suppose that 11% of adolescent females in the United States have iron deficiency. In a random sample of 300 adolescent females in the United States, what is the probability less than 8% of the females in the sample have iron deficiency? 0.0484 12) Which of the following statements about the t t distribution is/are true?The t t distribution is used in confidence intervals for a population mean when σ σ is estimated with s s .As the sample size increases, the t t distribution gets closer to a standard normal distribution.There t t distribution is the same regardless of the sample size. 1&2 only

13) The army reports that the distribution of head circumference among male soldiers is approximately normal with μ=22.8 inches and σ=1.1 inches. The army plans to make helmets in advance to fit the middle 98% of head circumferences for male soldiers. Soldiers who fall outside this range will get custom-fitted helmets. What head circumferences will not require custom fitted helmets? (20.24, 25.36) 14) The 2018 General Social Survey asked, “What do you think is the ideal number of children for a family to have?” From a sample of 1357 people, the mean was 2.61 with a standard deviation of 0.94. A 90% confidence interval for the true mean number of children people think a family should have is (2.568, 2.652). What is the width for this confidence interval?0.10 0.084 15) Suppose that across all departments at a large university with over 500 faculty, 25% are female. A SRS of 10 faculty members is selected and the total number of females is counted (out of the 10). Does this constitute a binomial experiment? Yes, all the conditions are met. 16) An online retailer claims 90% of all orders are shipped within 12 hours of being received. Let p^ p^ be the sample proportion of orders that are shipped within 12 hours in a SRS of orders. What is the minimum sample size required for p^ p ^to be approximately normally distributed? 100 17) Four of the 20 students (20%) in a class are fraternity or sorority members. A random sample of 5 students in the class is taken and the number of students in the sample who are fraternity or sorority members is counted (out of the 5). Does this constitute a binomial experiment? No, the probability of success is not constant from trial to trial. 18) A wildlife biologist wants to determine the mean weight of adult red squirrels. She captures 10 squirrels she believes to be representative of the species and weighs them, finding a mean of 12.32 grams and standard deviation of 1.88gm. Assuming these squirrels can be considered a random sample of all red squirrels, which of the following formulas gives a 95% confidence interval for the mean weight of all squirrels? 12.32±2.262(1.88/ root 10) 19) An actuary is interested in estimating the proportion of young adults who plan to have children someday. She takes a SRS of 60 young adults and finds that 48 of them plan to have children. Construct a 95% confidence interval for the proportion of young adults who plan to have children someday. (0.699, 0.901) 20 ) The accuracy of the Normal approximation to the binomial improves when: the number of observations, n n , increases. 21) Suppose that 11% of adolescent females in the United States have iron deficiency. In a random sample of 300 adolescent females in the United States, what is the probability more than 8% of the females in the sample have iron deficiency? 0.9516 22) Arsenic is a compound naturally occurring in very low concentrations. Arsenic blood concentrations in healthy individuals are normally distributed with a mean of 3.2 mg/dl and standard deviation of 1.5 mg/dl. Determine the required sample size to construct a 95% confidence interval to within +/- 0.5 mg/dl of the population mean. 36 21) Suppose X ∼ N (73,3) X ∼ N (73,3). What is P(67<X<73) P (67< X <73)? 0.4772 22) Which of the following will reduce the margin of error in a confidence interval? All the other answers are correct 23) An article described a study of a random sample of young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 34.6% of the participants. They constructed the following 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums: (0.217,0.475)(0.217,0.475) What was the margin of error for their confidence interval? 0.129 24) Which of the following statements about the t t distribution is/are true?

1 & 2 only 25) Suppose 2% of American females aged 15-19 are pregnant. In a random sample of 50 females between the ages of 15 and 19, what is the probability that exactly 1 is pregnant? 0.3716 26) The histogram below shows the distribution of a population with mean μ=4 μ =4 and standard deviation σ=2.828 σ =2.828 the sampling distribution of the sample mean will be right skewed. 27) The 2018 General Social Survey asked, “What do you think is the ideal number of children for a family to have?” From a sample of 1357 people, the mean was 2.61 with a standard deviation of 0.94. How many people should be sampled to get a 95% confidence interval with a width of 0.05? 5656 28) A recent poll indicates that 48% of all registered voters in America plan to vote for a specific candidate in the upcoming presidential election. If a random sample of 30 voters were taken, would it be appropriate to use the Normal approximation to find the probability that less than 15 of them plan to vote for the candidate? Yes, because the sample size condition is met and a random sample was taken. 30) The average number of acres burned by wildfires in the United States is 780 acres with standard deviation 500 acres. Since some wildfires burn thousands of acres, the distribution of acres burned by wildfires is strongly right skewed. Suppose a SRS of 100 wildfires is taken. Find the probability that the sample mean number of acres burned is greater than 820 acres. 0.2119 31) Let X X be the cholesterol level of a randomly chosen individual. Assume that cholesterol levels are approximately Normally distributed with mean μ=203 μ =203 and standard deviation σ=20 σ =20. Let be the sample mean cholesterol level of a randomly chosen sample of 25 individuals. Between which two values would the middle 96% of sample means fall? 194.8 and 211.2 32) Which of the following are true of p^ All of the other answers are correct. p ^ is a statistic p ^ is a quantitative random variable p ^ describes categorical data 42) Morty is taking a quiz with 5 true/false questions, and he did not study. Assume the questions each cover different topics and can be considered independent. He has knowledge of some topics while he knows nothing about other topics, so the probability he will get the answer correct varies from question to question. Does the number of questions Morty answers correctly follow a binomial distribution? No, the probability of success is not constant from trial to trial. 43)A SRS of 40 male college students is taken and 8 of them wear an earring. Are the conditions met to construct a 95% confidence interval for the true proportion of male college students who wear an earring? No, because although the data was gathered randomly, np^<10 42) The 2018 General Social Survey asked, “What do you think is the ideal number of children for a family to have?” From a sample of 1357 people, the mean was 2.61 with a standard deviation of 0.94. How many people should be sampled to get a 95% confidence interval with a margin of error of 0.05? 1414 43) Which of the following is true of p^ p ^ is a quantitative random variable 44) Suppose 2% of American females aged 15-19 are pregnant, and a random sample of 100 American females aged 15-19 is taken. Would it be appropriate to use the normal approximation to the binomial to calculate the probability that 8 or fewer are pregnant? No, because the sample size condition is not met. 45) Suppose that 71% of all college women have been on a diet in the past 12 months. Suppose we set our sample size to be n n = 100. What is the probability of choosing a SRS in which between 62% and 68% of the college women have been on a diet within the past 12 months? 0.2306

46) Each of the 110 students in a statistics class selects a different random sample of 35 quiz scores from a population of 5000 scores they are given. Using their data, each student constructs a 90% confidence interval for μ μ , the average quiz score of the 5000 students. Which of the following conclusions is correct? About 90% of the confidence intervals will contain μ μ 47) Getting an adequate amount of sleep can improve a variety of physiological functions, and it is known that the average number of hours that people sleep each night is Normally distributed. A psychiatrist at a major research center takes an SRS of 25 emotionally disturbed patients and records the average amount of sleep that each gets on a typical night Suppose a 90% confidence interval for the mean amount of time that emotionally disturbed patients sleep during a typical night is (6.6,7.2)(6.6,7.2) Interpret this interval in the context of the problem We are 90% confident that the mean hours of sleep that emotionally disturbed patients get on a typical night is in this interval. 50) The accuracy of the Normal approximation to the binomial improves when: the number of observations, n n , increases. 51) An actuary is interested in estimating the proportion of young adults who plan to have children someday. She takes a SRS of 60 young adults and finds that 48 of them plan to have children. Construct a 90% confidence interval for the proportion of young adults who plan to have children someday. (0.715, 0.885) 52) In a random sample of size 10, we have a mean of 23 and a standard deviation of 4. Assuming the conditions are met, what is a 95% confidence interval for the population mean? (20.14, 25.86) 53) Four of the 20 students (20%) in a class are fraternity or sorority members. A random sample of 5 students in the class is taken and the number of students in the sample who are fraternity or sorority members is counted (out of the 5). Does this constitute a binomial experiment? Incorrect answer: No, the probability of success is not constant from trial to trial. 54) An online retailer claims 90% of all orders are shipped within 12 hours of being received. Let p^ p ^ be the sample proportion of orders that are shipped within 12 hours in a SRS of orders. What is the minimum sample size required for p^ p ^ to be approximately normally distributed? 100 55) Suppose that across all departments at a large university with over 500 faculty, 25% are female. A SRS of 10 faculty members is selected and the total number of females is counted (out of the 10). Does this constitute a binomial experiment? Yes, all the conditions are met. 56) Which of the following statements about the t t distribution is/are true? 1&2 57 )Suppose that 11% of adolescent females in the United States have iron deficiency. In a random sample of 300 adolescent females in the United States, what is the probability less than 8% of the females in the sample have iron deficiency? 0.0484 58) Viral hepatitis occurs in 7% of patients who receive multiple blood transfusions during heart surgery. A SRS was taken of 200 heart surgery patients who had multiple blood transfusions. If appropriate, use the normal approximation to the binomial to find the probability that at least 10 contracted viral hepatitis. 0.8662 59 ) An insurance company knows that in the entire population of millions of insured workers, the distribution of annual cost of workers’ compensation claims is right skewed with a mean $439 per insured worked and standard deviation $20,000. Suppose a sample of 20 workers’ compensation claim costs is taken. What is the probability that the sample mean cost is greater than $1500? This probability cannot be calculated because we do not know the sampling distribution of xˉ 60) The time that it takes a randomly selected rat of a certain subspecies to find its way through a maze is normally distributed with mean μ=1.5 μ =1.5 minutes and σ=0.35 σ =0.35

minutes. Suppose 4 rats are selected. What is the probability that the sample mean time to navigate the maze is more than 1.92 minutes? 0.0082 61 )With larger sample sizes there is a greater likelihood that the data distribution… will look similar to the population distribution. 62)The mean amount of money spent on health insurance per month by US citizens is strongly right skewed with a mean of $456 and standard deviation of $53. Suppose a SRS of 50 US citizens is taken. Find the probability that the sample mean amount of money spent on health insurance is less than $430/month. 0.0003 62) An online retailer claims 90% of all orders are shipped within 12 hours of being received. Let p^ p ^be the sample proportion of orders that are shipped within 12 hours in a SRS of orders. Suppose we set our sample size to n=120 n =12. What is the probability of selecting an SRS in which less than 105 orders were shipped within 12 hours? 0.1807 63) Suppose it is known that 10% of adolescent females in the United States have iron deficiency. In a random sample of 35 adolescent females, what is the probability that exactly 3 have iron deficiency? 0.225 64) The confidence level C C of a confidence interval is the probability that the confidence interval method works to capture the true value of the parameter of interest. 65) An online retailer claims 90% of all orders are shipped within 12 hours of being received. Let \hat{p} p ^ be the sample proportion of orders that are shipped within 12 hours in a SRS of orders. What is the minimum sample size required for \hat{p} p ^ to be approximately normally distributed? 66) The weight of a particular variety of watermelon is known to be Normally distributed with mean 14.2 and standard deviation 0.66. What is the probability a randomly selected watermelon weighs between 14 and 15 pounds? 0.5063 67) The development of viral hepatitis subsequent to blood transfusion can cause serious complications for a patient. This occurs in 7% of patients who receive multiple blood transfusions during heart surgery. A SRS was taken of 33 heart surgery patients who had multiple blood transfusions. Find the probability that at least 2 contracted viral hepatitis. 0.6823 The development of viral hepatitis subsequent to blood transfusion can cause serious complications for a patient. This occurs in 7% of patients who receive multiple blood transfusions during heart surgery. A SRS was taken of 33 heart surgery patients who had multiple blood transfusions. Find the probability that more than 2 contracted viral hepatitis. 0.4095 70) The proportion of baby boys born in the United States is equal to 0.512. The two histograms below represent repeated samples of newborn babies in the United States. What is the best explanation the difference in the spread of the distributions? Different sample sizes are being used. 71) According to the CDC National Center for Health Statistics, about 42.4% of adult Americans fit the medical definition of being obese. How large would a sample from this population need to be to ensure that the distribution of the sample proportion is approximately Normal? 24 72) A neurologist randomly samples 400 adult men in the United States and finds that 29 of them have experienced at least one migraine headache. Construct a 99% confidence interval for the proportion of adult men in the United States who have experienced at least one migraine headache. (0.039, 0.106) 73) In the US, we categorize adolescent girls as either anemic, border line anemic or as having a normal level of iron in their blood. Suppose 10% of adolescent girls are anemic, 15% are border line anemic and the rest have normal iron levels in their