THIS IS FOR STATS PLEASE ANSWER CLEARLY DIGITALLY

Q1

A data set includes systolic blood pressure measurements from 147 adult females. If we compute the values of sample statistics from that sample, which of the following statistics are unbiased estimators of the corresponding population parameters? Select all that apply. D A. Sample median D B. Sample variance Cl C. Sample mean D D. Sample range D E. Sample proportion D F. Sample standard deviation 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? Choose the correct answer below. {1:} A. Yes; the sample size is over 50, so the sample of incomes will be normally distributed. f} B. No; unless more than 50 samples are collected, the sample of incomes will not be normally distributed. {1:} C. No; the sample means will be normally distributed, but the sample of incomes will be skewed to the right. {:2- D. No; the population of incomes is not normally distributed, so the sample means will not be normally distributed for any sample size. 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 = 4.7 kg. Complete parts (a) through (c) below. (I) 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 4 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? A. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size. (":3 B. Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size. C. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sampte size. 1"} D. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. When women were finally allowed to become pilots of ghterjets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ejection seats were designed for men weighing between 140 lb and 191 lb. Weights of women are now normally distributed with a mean of 165 lb and a standard deviation of 36 lb. Complete parts (a) through (c) below. (E a. If 1 woman is randomly selected, find the probability that her weight is between 140 lb and 191 lb. The probability is approximately |:|. (Round to four decimal places as needed.) b. if 30 different women are randomly selected, nd the probability that their mean weight is between 140 lb and 191 lb. The probability is approximately |:|. (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? {:2- A. The part (b) probability is more relevant because the seat performance for a single pilot is more important. {I} B. The part (b) probability is more relevant because the seat performance for a sample of pilots is more important. {:22- C. The part (a) probability is more relevant because the seat performance for a sample of pilots is more important. {I} D. The part (a) probability is more relevant because the seat performance for a single pilot is more important. A researcher collects a simple random sample of gradepoint 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? (E- Select all that apply. I] A. If the population of statistics students has a normal distribution. I] B. The sample has more than 30 grade-point averages. I] C. The researcher collects more than 30 samples. I] D. If the population of grade-point averages has a normal distribution