Question

1. 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 136. What is the probability that the sample proportion will be at least 5 percentage points higher than the population proportion?

2. Based on historical data, your manager believes that 34% of the company's orders come from first-time customers. A random sample of 91 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is greater than than 0.41?

Answer 1

We would be looking at Q1 here.

Q1) Given that the proportion of settled complaints received is 0.75, the distribution of the sample proportion of sample size n = 136 is modelled here as:

The probability that that the sample proportion will be at least 5 percentage points higher than the population proportion is computed here as:

P( p > 0.75 + 0.05)

= P( p > 0.8)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.0891 is the required probability here.