Question

1)A population of values has a normal distribution with μ=74.3μ=74.3 and σ=37.4σ=37.4. You intend to draw a random sample of size n=137n=137.

Find the probability that a single randomly selected value is less than 72.1.
P(X < 72.1) =

Find the probability that a sample of size n=137n=137 is randomly selected with a mean less than 72.1.
P(¯xx¯ < 72.1) = (Enter your answers as numbers accurate to 4 decimal places.)

2)CNNBC recently reported that the mean annual cost of auto insurance is 972 dollars. Assume the standard deviation is 229 dollars. You take a simple random sample of 94 auto insurance policies.

Find the probability that a single randomly selected value is less than 996 dollars.
P(X < 996) =

Find the probability that a sample of size n=94n=94 is randomly selected with a mean less than 996 dollars.
P(¯xx¯ < 996) = (Enter your answers as numbers accurate to 4 decimal places.)

3)Suppose the true proportion of voters in the county who support a new fire district is 0.49. Consider the sampling distribution for the proportion of supporters with sample size n = 177.

What is the mean of this distribution?  (Enter your answer accurate to two decimal places.)

What is the standard deviation of the sampling distribution (i.e. the standard error)?     (Enter your answer accurate to three decimal places.)

4)Suppose that the efficacy of a certain drug is 0.51. Consider the sampling distribution (sample size n = 192) for the proportion of patients cured by this drug.

What is the mean of this distribution?  (Enter your answer as a number accurate to 2 decimal places.)

What is the standard deviation of this sampling distribution (i.e., the standard error)?     (Enter your answer as a number accurate to 3 decimal places.)

5)Data from the U.S. Department of Education indicates that 35% of business graduate students from private universities had student loans. Suppose you randomly survey a sample of graduate business students from private universities. Consider the sampling distribution (sample size n = 214) for the proportion of these students who have loans.

What is the mean of this distribution?  (Enter your answer accurate to two decimal places.)

What is the standard deviation of this sampling distribution (i.e., the standard error)?     (Enter your answer accurate to three decimal places.)

Answer 1