Question

1. A population of values has a normal distribution with μ=72μ=72 and σ=3.1σ=3.1. You intend to draw a random sample of size n=154n=154.

Find the probability that a single randomly selected value is between 71.3 and 71.7.
P(71.3 < X < 71.7) =

Find the probability that a sample of size n=154n=154 is randomly selected with a mean between 71.3 and 71.7.
P(71.3 < M < 71.7) =

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.

2.

In a recent year, the Better Business Bureau settled 75% of complaints they received. (Source: USA Today, March 2, 2009) You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Assume the population proportion of complaints settled for the computer stores is the 0.75, as mentioned above. Suppose your sample size is 278. What is the probability that the sample proportion will be at least 5 percent more than the population proportion?

Note: You should carefully round any z-values you calculate to at least 4 decimal places to match wamap's approach and calculations.

Answer =

(Enter your answer as a number accurate to 4 decimal places.)

3.

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 165000 dollars. Assume the standard deviation is 32000 dollars. Suppose you take a simple random sample of 90 graduates.

Find the probability that a single randomly selected salary that doesn't exceed 169000 dollars.
Answer =

Find the probability that a sample of size n=90n=90 is randomly selected with a mean that that doesn't exceed 169000 dollars.
Answer =

Enter your answers as numbers accurate to 4 decimal places.

Thank You

Answer 1

1) a) Given

b) Given

2) The probability that the sample proportion will be at least 5 percent more than the population proportion is

3) a) The probability that a single randomly selected salary that doesn't exceed 169000 dollars is

Given

b) The probability that a sample of size n=90 is randomly selected with a mean that that doesn't exceed 169000 dollars is