THIS IS FOR STATS PLEASE ANSWER CLEARLY AND Digitally

Q1

Which of the following is NOT a property of the sampling distribution of the sample mean? (E Choose the correct answer below. The sample means target the value of the population mean. The expected value of the sample mean is equal to the population mean. The distribution of the sample mean tends to be skewed to the right or left. POP? The mean of the sample means is the population mean. Annual incomes of statistics students are known to have a distribution that is skewed to the right instead of being normally distributed. Assume that we collect a random sample of annual incomes of 50 statistics students. Can the distribution of incomes in that sample be approximated by a normal distribution because the sample is large? Why or why not? (E- Choose the correct answer below. {:2- A. Yes; the sample size is over 50, so the sample of incomes will be normally distributed. ('1- B. No; the population of incomes is not normally distributed, so the sample means will not be normally distributed for any sample size. a") C. No; unless more than 50 samples are collected, the sample of incomes will not be normally distributed. D. No; the sample means will be normally distributed, but the sample of incomes will be skewed to the right. An elevator has a placard stating that the maximum capacity is 4100 |b~27 passengers. So, 27 adult male passengers can have a mean weight of up to 4100/27 = 152 pounds. Assume that weights of males are normally distributed with a mean of 182 lb and a standard deviation of 38 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 152 lb. b. Find the probability that a sample of 27 randomly selected adult males has a mean weight greater than 152 lb. c. What do you conclude about the safety of this elevator? (E a. The probability that 1 randomly selected adult male has a weight greater than 152 lb is D. (Round to four decimal places as needed.) b. The probability that a sample of 27 randomly selected adult males has a mean weight greater than 152 lb is D. (Round to four decimal places as needed.) c. Does this elevator appear to be safe? A researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. Under what conditions can that sample mean be treated as a value from a population having a normal distribution? Select all that apply. D A. The sample has more than 30 grade-point averages. D B. The researcher collects more than 30 samples. Cl C. If the population of gradepoint averages has a normal distribution. El D. If the population of statistics students has a normal distribution. Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of p = 1.3 kg and a standard deviation of o = 5.6 kg. Complete parts (a) through (c) below. (E a. If 1 male college student is randomly selected, nd the probability that he gains between 0 kg and 3 kg during freshman year. The probability is D. (Round to four decimal places as needed.) b. if 25 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg. The probability is D. (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? {1:} A. Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size. ("E B. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. {"j} C. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. 1"} D. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size. C? A. Yes, because there is a good chance that 27 randomly selected people will not exceed the elevator capacity. {"3- B. No, because there is a good chance that 27 randomly selected adult male passengers will exceed the elevator capacity. {I} C. No, because 27 randomly selected people will never be under the weight limit. {ji- D. Yes, because 27 randomly selected adult male passengers will always be under the weight limit