# z score based percentage and confidence interval

1. The U.S. Department of Transportation reported the results of a survey of driving safety. In a random sample of 900 drivers, 425 were using their cell phone. Compute,and explain, a 95% confidence interval estimate of the population proportion of drivers who use their cell phone while driving.

2. Grades on a final exam in Statistics are normally distributed with a mean of 73 and a standard deviation of 8.

A) What is the probability that a student will receive a score greater than 90?

B) If the top 5% of scores receive a grade of "A", what is the minimum score that a student will need to get an "A"?

3. The population distribution of the number of semester hours of college credit taken by first-time candidates for the CPA exam has a mean of 130 hours and a standard deviation of 24 hours. A random sample of 95 first-time candidates for the CPA exam is to be taken for further study.

A) What is the shape, mean, and standard deviation of the sampling distribution of the sample mean for samples of size 95?

B) What is the probability that a sample of 95 will show a sample mean greater than 136 semester hours?

4. An Airline wants to estimate the average number of unoccupied seats per flight. A random sample of 175 flights is selected and the mean number of unoccupied seats is 11.6. Assume that the population standard deviation of unoccupied seats is known to be 3.9. Compute, and explain, a 95% confidence interval estimate of the population mean number of unoccupied seats per flight.

5. Two percent (.02) of the items produced by a machine are defective. A random sample of 500 items is selected and checked for defects.

A) what is the probability that the sample will contain 3% or more defective items?

6. Health Insurers are putting pressure on hospitals to reduce the average "length of stay" of their patients. A random sample of 20 hospitals in one state had a mean "length of stay" for women of 3.9 days, and a standard deviation of 2.1 days. Compute, and explain, a 98% confidence interval estimate of the population mean "length of stay" for women in that state.

7. Assume that the population proportion of all business professionals who select an airline based on price is 0.27. A random sample of 325 business professionals is to be taken for further study.

A) What is the shape, mean, and standard deviation of the sampling distribution of the sample proportion for samples of size 325.

B) What is the probability that our sample of 325 results in a sample proportion that falls within 4 percent of the population value ( ± .04)?

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#### Solution Preview

Hi there,

I've included my answers for the first 4 questions.

1. The U.S. Department of Transportation reported the results of a survey of driving safety. In a random sample of 900 drivers, 425 were using their cell phone. Compute,and explain, a 95% confidence interval estimate of the population proportion of drivers who use their cell phone while driving.

The critical value for 95% is 1.96.

Proportion of drivers who use their cells: 425/900=0.4722.

Margin of error=1.96*sqrt[0.4722*(1-0.4722)/900]=0.0326

The 95% confidence interval ...

#### Solution Summary

The solution provides detailed explanation how to solve z score based probability and find the confidence interval.