Note: For any part below, if it cannot be answered, enter DNE. Read the directions carefully and pay attention to the different sample sizes. In this problem, round to 4 decimal places.

A quality control company was hired to study the length of meter sticks produced by a certain company. The team carefully measured the length of many many meter sticks, and the distribution seems to be slightly skewed to the right with a mean of 99.83 cm and a standard deviation of 0.15 cm.

a) What is the probability of finding a meter stick with a length of more than 99.94 cm?

b) What is the probability of finding a group of 44 meter sticks with a mean length of less than 99.81 cm?

c) What is the probability of finding a group of 38 meter sticks with a mean length of more than 99.85 cm?

d) What is the probability of finding a group of 36 meter sticks with a mean length of between 99.82 and 99.84 cm?

e) For a random sample of 32 meter sticks, what mean length would be at the 92nd percentile?