CNNBC recently reported that the mean annual cost of auto insurance is 990 dollars. Assume the standard deviation is 293 dollars. You take a simple random sample of 84 auto insurance policies.Find the probability that a single randomly selected value is less than 992 dollars.P(x<992)=Find the probability that a sample of sizen=84is randomly selected with a mean less than 992 dollars.P(x<992)=Enter your answers as numbers accurate to 4 decimal places.

2...A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 28.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 28.5 weeks and that the population standard deviation is 4.8 weeks. Suppose you would like to select a random sample of 157 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 27.5 and 29.6.

P(27.5

Find the probability that a sample of size

n=157

is randomly selected with a mean between 27.5 and 29.6.

P(27.5

Enter your answers as numbers accurate to 4 decimal places.

3::::

On the distant planet Cowabunga , the weights of cows have a normal distribution with a mean of 457 pounds and a standard deviation of 68 pounds. The cow transport truck holds 6 cows and can hold a maximum weight of 3054. If 6 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 3054? (This is the same as asking what is the probability that their mean weight is over 509.)