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 99.89 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 100.05 cm?
b) What is the probability of finding a group of 50 meter sticks with a mean length of less than 99.88 cm?
c) What is the probability of finding a group of 34 meter sticks with a mean length of more than 99.92 cm?
d) What is the probability of finding a group of 24 meter sticks with a mean length of between 99.88 and 99.92 cm?
e) For a random sample of 48 meter sticks, what mean length would be at the 92nd percentile?
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