Question

A population of values has a normal distribution with μ=176.9 and σ=81. You intend to draw a random sample of size n=181.
Find the probability that a sample of size n=181 is randomly selected with a mean between 178.1 and 178.7.
P(178.1 < M < 178.7) =
Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 29.1 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 29.1 weeks and that the population standard deviation is 8.4 weeks. Suppose you would like to select a random sample of 62 unemployed individuals for a follow-up study.
Find the probability that a single randomly selected value is between 29.5 and 30.5.
P(29.5 < X < 30.5) =
Find the probability that a sample of size n=62 is randomly selected with a mean between 29.5 and 30.5.
P(29.5 < M < 30.5) =

CNNBC recently reported that the mean annual cost of auto insurance is 1011 dollars. Assume the standard deviation is 250 dollars. You take a simple random sample of 95 auto insurance policies.
Find the probability that a single randomly selected value is less than 985 dollars.
P(X < 985) =
Find the probability that a sample of size n=95 is randomly selected with a mean less than 985 dollars.
P(M < 985) =

Answer 1