Name:_____________________________________________ Date:__________________________ Week 7 Quiz Quiz to be turned in next week at the beginning of class. Find the following probabilities. Use drawings to assist you when necessary. Round all probabilities to 4 decimal places. 1. P(z > 1.37) Answer:_____________ 2. P(z < 2.92) Answer:_____________ 3. Answer:_____________ Finding z-scores for given areas. Round all z-scores to 2 decimal places. 4. Find the z-score with an area of 0.9824 to its left 5. Find the z-score with an area of 0.6276 to its right P(0.38 z 2.11) The Twilight Theater chain has collected data over the last 5 years to determine how much money their customers spend on concessions. The study revealed that the spending distribution is approximately normally distributed with a mean of $7.25 and a standard deviation of $2.75. 6. What percentage of customers spend less than $5.00 on concessions? Round your answer to a tenth of a percent. 7. The company believes that if they target those customers that spend in the lowest 10%, they can increase their revenue and thus there profits. What spending amount is the 10th percentile that they wish to target? Round your answer to two decimal places. 8. In a random sample of 250 college students, 60 admitted to cheating on an exam during their freshman year. a. Construct a 98% confidence interval for the proportion of students admitting to cheating on an exam their freshman year. Round the limits for the confidence interval to 3 decimal places. b. Using the confidence interval from (b), can you conclude that a majority of students cheat on an exam during their freshman year? Explain. 9. According to USA Today (May 14, 2002), the national figure for all drivers who use their seat belts is 85%. You wish to conduct your own survey in San Antonio to determine what proportion of the drivers use seat belts. Find the necessary sample size if you want your estimate to be within 0.02, with 95% confidence. Use the national figure of 85% for your initial estimate of p . 10. An art insurance agent wants to estimate the mean dollar value of all of a local artist's paintings. The agent takes a sample of 15 of the artist's paintings and gets them assessed by a reputable art dealer. The mean value of the sample is $2,458 with a standard deviation of $376. a. Find a 95% confidence interval for the mean dollar value of all of the artist's paintings. b. Interpret the confidence interval from step (a)