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. 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