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 246. What is the probability that the sample proportion will be at least 4 percentage points higher 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.)

According to a 2009 Reader's Digest article, people throw away approximately 15% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 138 grocery shoppers to investigate their behavior. What is the probability that the sample proportion is between 0.06 and 0.14? Note: You should carefully round any intermediate values you calculate to 4 decimal places to match wamap's approach and calculations. Answer = (Enter your answer as a number accurate to 4 decimal places.)

Based on historical data, your manager believes that 30% of the company's orders come from first-time customers. A random sample of 193 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.29 and 0.48? Note: You should carefully round any z-values you may calculate to 4 decimal places to match wamap's approach and calculations. Answer = (Enter your answer as a number accurate to 4 decimal places.)

Answer 1

Solution:-

1) The probability that the sample proportion will be at least 4 percentage points higher than the population proportion is 0.0737 .

p = 0.75, n = 246

By applying normal distribution:-

z = 1.449

P(z > 1.449) = 0.0737

2) The probability that the sample proportion is between 0.06 and 0.14 is 0.3696 .

p = 0.15, n = 138

By applying normal distribution:-

z₁ = - 2.96

z₂ = - 0.329

P( - 2.96 < z < - 0.329) = P(z > - 2.96) - P(z > - 0.329)

P( - 2.96 < z < - 0.329) = 0.9985 - 0.6289

P( - 2.96 < z < - 0.329) = 0.3696