There are 4 questions. 1;A random variable is normally distributed with mean μ=$1500 and standard deviation ∂=$100. Determine the standard error of the sampling distribution of the mean for sample random samples with the following sample sizes; a. n=16 b. n=100 c. n=400 d. n=1000 2;It has been reported that the average U.S. teenager sends 80 text masseges per day. For purposes of this exercise, we will assume the daily number of text messages sent is normally distributed with a standard deviation of 15.0 messages. For a randomly selected group of 10 teenagers, and considering these persons to be a simple random sample of all U.S. teens,what is the probablity that the group will send at least 900 text messages next Wednesday? 3; According to the Investment Company Institute, 40% of U.S. households have an Individual Retirement Account. Assuming the population proportion to be π=0.4 and that a simple random sample of 400 hhouseholds has been selected; a.What is the expected value of p=the proportion in the sample having IRA? b. What is the standard error of the sampling distribution of the proportion? c.What is the probability that at least 35% of those in the sample will have an IRA? d.What is the probability that between 38% and 45% of those in the sample will have an IRA? 4;In 2009, the average fee paid by H&R Block tax preparation customers was $187. Assume that the standard deviation of fees was $60 but that we have no idea regarding the shape of the population distribution. a.What additional assumption about the popultion would be needed in order to use the standard normal table in determining the probability that the mean fee for a simple random sample of 5 customers was less than $170? b.What is the probability that the mean fee for a simple random sample of 36 customers was less than $170? What role does the central limit theorem play in making it possible to determine this probability? Thank you