AP Statistics Normal Applications using the calculator Name_____________________________ 1. The Speedmaster IV automobile gets an average of 22 miles per gallon in the city. The standard deviation is 3 miles per gallon. Assume the variable is normally distributed. Find the probability that on any given day, the car will get more than 26 miles per gallon when driven in the city. 2. The average age of CEO’s is 56 years. Assume the variable is normally distributed. If the standard deviation is four years, find the probability that the age of a randomly selected CEO will be between 53 and 59 years. 3. The average amount of snow per season in Trafford is 44 inches. The standard deviation is 6 inches. Find the probability that Trafford will receive at least 53 inches of snow that next year. Assume the variable is normally distributed. 4. In order to qualify for letter sorting, applicants are given a speed-reading test. The scores are normally distributed, with a mean of 80 and a standard deviation of 8. The variable is also normally distributed. If only the top 15% of the applicants are selected, find the cutoff score. 5. In order to help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 5% of the students in the district, based on the scores on a reading achievement exam. If the average score for the students in the district is 122.6, find the cutoff score that will make a student eligible for the program. The standard deviation is 18. Assume the variable is normally distributed. 6. Given a normal distribution with a mean of 25, what is the standard deviation if 18% of the values are above 29? 7. Given a normal distribution with a standard deviation of 10, what is the mean if 21% of the values are below 50? 8. Given a normal distribution with 80% of the values above 125 and 90% of the values above 110, what are the mean and standard deviation? 9. It 75% of all families spend more than $75 weekly for food, while 15% spend more than $150, what is the mean weekly expenditure and what is the standard deviation? 10. A coffee machine can be adjusted to deliver any fixed number of ounces of coffee. If the machine has a standard deviation in delivery equal to 0.4 ounce, what should be the mean setting so than an 8-ounce cup will overflow only 0.5% of the time?