Help me with the attached Problems.
13. The meanamount 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 deviationof $10. What is the probabilityof selecting a credit card customer at random and finding the customer charged between $70 and $83?
14. A statisticsstudent receives a grade of 85 on a statisticsmidterm. 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 surveyat 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 errorof 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?
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
This solution solves normal distribution probability problems.