Question 1: Letxbe a continuous random variable that has a normal distribution with=85and=16.AssumingnN0.05,find the probability that the sample mean,x,for a random sample of19taken from this population will be less than82.0.

Round your answer to four decimal places.

Question 2: in a population of23,700subjects,32%possess a certain characteristic. In a sample of340subjects selected from this population,30%possess the same characteristic. How many subjects in the population and sample, respectively, possess this characteristic?

Enter you answer; How many subjects in the population possess this characteristic?subjects in the population possess the characteristic

Enter you answer; How many subjects in the sample possess this characteristic?subjects in the sample possess the characteristic

Question 3:According to a poll,55%of Americans do not know that GOP stands for Grand Old Party (Time, October 17, 2011). Assume that this percentage is true for the current population of Americans. Letp^be the proportion in a random sample of521Americans who do not know that GOP stands for Grand Old Party. Find the mean and standard deviation of the sampling distribution ofp^and describe its shape.

Round your answer for the standard deviation to four decimal places.

p^=Enter you answer; mean

p^=