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# Normal Distribution, Probability and Mean

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13. The mean amount of gasoline and services charged by Key Refining Company credit customers is \$70 per month. The distribution of amounts spent is approximately normal with a standard deviation of \$10. What is the probability of selecting a credit card customer at random and finding the customer charged between \$70 and \$83?

14. A statistics student receives a grade of 85 on a statistics midterm. If the corresponding z-score equals +1.5 and the standard deviation equals 7, what is the average grade on this exam?

15. A sample of 500 evening students revealed that their annual incomes from employment in industry during the day were normally distributed with a mean income of \$30,000 and a standard deviation of \$3,000. How many students earned more than \$30,000?

16. A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the standard error of the mean? 10

17. The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a person would score 130 or more on the test?
.9772

18. Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. What is the probability that a tire will last 72,000 miles or more? 0.9987