1. Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.2. (Round your answers to four decimal places.)
(a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 12 pins is at least 51?
(b) What is the (approximate) probability that the sample mean hardness for a random sample of 37 pins is at least 51?
2. Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 8 min and standard deviation 4 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (Round your answer to four decimal places.)
3. There are 40 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 6 min and a standard deviation of 4 min. (Round your answers to four decimal places.)
(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?
(b) If the sports report begins at 11:10, what is the probability that he misses part of the report if he waits until grading is done before turning on the TV?