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 meter sticks, and the distribution seems to be severely skewed to the right with a mean of 99.84 cm and a standard deviation of 0.2 cm.
a) What is the probability of finding a meter stick with a length of more than 100.04 cm? ____
b) What is the probability of finding a group of 42 meter sticks with a mean length of less than 99.82 cm?_____
c) What is the probability of finding a group of 50 meter sticks with a mean length of more than 99.87 cm? _____
d) What is the probability of finding a group of 28 meter sticks with a mean length of between 99.82 and 99.86 cm? ______
e) For a random sample of 32 meter sticks, what mean length would be at the 92nd percentile? ______
