Question

1. Based on historical data, your manager believes that 31% of the company's orders come from first-time customers. A random sample of 82 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.28?

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

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 102. What is the probability that the sample proportion will be at least 3 percent more than the population proportion?

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

3. Based on historical data, your manager believes that 27% of the company's orders come from first-time customers. A random sample of 186 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.32?


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

Answer 1

1) Given data

population proportion (p)=0.31

Number of sample (n)=82

Sample proportion

test statistic for this proportion will be

So the probability of getting sample proportion less than 0.28 will be the probability less than Z= -0.59 from the Standard probability distribution table for Z score

So

P=0.2776

2) Given data

population proportion (p)=0.75

Number of sample (n)=102

Sample proportion

test statistic for this proportion will be

So the probability of getting sample proportion at most  0.78 will be the probability less than Z= 0.70  from the Standard probability distribution table for Z score

that is

So probability of getting proportion at least 0.78 will be

3) Given data

population proportion (p)=0.27

Number of sample (n)=186

Sample proportion

test statistic for this proportion will be

So the probability of getting sample proportion less than 0.32  will be the probability less than Z= 1.54 from the Standard probability distribution table for Z score

So

P=0.9377