Note: For any part below, if it cannot be answered, enter NA.

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 100.05 cm and a standard deviation of 0.11 cm.

a) What is the probability of finding a meter stick with a length of more than 100.16 cm?

b) What is the probability of finding a group of 42 meter sticks with a mean length of less than 100.04 cm? 

c) What is the probability of finding a group of 46 meter sticks with a mean length of more than 100.07 cm? 

d) What is the probability of finding a group of 28 meter sticks with a mean length of between 100.04 and 100.07 cm? 

e) For a random sample of 44 meter sticks, what mean length would be at the 92nd percentile?