Question

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 130. What is the probability that the sample proportion will be within 9 percentage points of the population proportion? Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer 1

P = Population Proportion = 0.75

So,

Q = 1 - P = 0.25

n = Sample Size = 130

Z = 0.09/0.0380

= 2.3698

By Technology, Cumulative Area Under Standard Normal Curve corresponding to Z = 2.3698 = 0.9911

So,

Area from mid value to one side = 0.9911 - 0.5 = 0.4911

So,

Total area from mid value to both sides = 0.4911 X 2 = 0.9822

So,

The probability that the sample proportion will be within 9 percentage points of the population proportion = 0.9822

So,

Answer is:

0.9822