1. Mr. Danny believes that the final exam grades for his statistics class have a normal distribution with a mean of 82 and a standard deviation of 8. (a) Find the score which separates the top 10% of the scores from the lowest 90% of the scores. (b) Mr. Danny plans to give all students who score in the top 10% of scores an A. Will a pupil who scored a 90 on the exam receive an A? Explain. (c) He also plans to give all pupils who score in the lowest 10% of scores an F. Will a student who scored a 65 on the exam receive an F? Explain. (d) If he decides to pass all pupils who score in the top 70% of scores, what will be the minimum score a pupil should have to pass the course?
2. Suppose that the talk time on the latest Androids is approximately normally distributed with mean 7 hours and standard deviation 0.8 hrs. (a) What proportion of the time will a fully charged iPhone last at least 6 hours? (b) What is the probability a fully charged android phone will last less than 5 hours? (c) What talk time would represent the cutoff for the top 5% of all talk times? (d) Would it be unusual for the phone to last more than 9 hours? Why
3. Suppose the scores earned on teacher Danny's maths exam are normally distributed with mean 64 and standard deviation 8. Danny wants too curve the exam scores as follows: The top 6% get an A, the next 14% get a B, the middle 60% get a C, the bottom 6% fail, and the rest earn a D. Any student who can determine these cut-offs earns five bonus points. Determine the cut-offs for teacher danny.