Discuss the below:
1)The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. a) what is the area between 415 pounds and the mean of 400 pounds? b) what is the area between the mean and 395 pounds? c) what is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?
2)Shorty's Muffler advertises they can install a new muffler in 30 minutes or less. However, the work standards department at corporate headquarters recently conducted a study and found that 20 percent of the mufflers were not installed in 30 minutes or less. The Maumee branch installed 50 last month. If the corporate report is correct: a) how many of the installations at the maumee branch would you expect more than 30 minutes? b) what is the likelihood that fewer than eight installations took more than 30 minutes? c) what is the liklihood that eight or fewer installations took more than 30 minutes? d) what is the liklihood that exactly 8 of the 50 installations took more than 30 minutes?
3)A study of long distance phone calls made from the corporate offices of the Pepsi Bottling Group, Inc., in Somers, New YOrk, showed the calls follow the normal distribution. The mean length of time per call was 4.2 minutes and the standard deviation was o.60 minutes. a) what fraction of the calls last between 4.2 and 5 minutes? b) what fraction of the calls last more thatn 5 minutes? c) what fraction of the calls last between 5 and 6 minutes? d) what fraction of the calls last between 4 and 6 minutes? e) as part of her report tot he president, the Director of Communications owuld like to report the length of the longest (in duration) 4 percent of the calls. What is this time?