When a certain manufacturing process is correctly adjusted, the length of a machine part produced is a random variable with a mean of 200 cm and a standard deviation of 0.1 cm. The individual measurements are normally distributed.
a) What is the probability that an individual part is longer than 200.2 cm?
b) Suppose a sample of 25 parts is chosen randomly. What s the probability that the mean of the sample is bigger than 200.2 cm?
c) Is it correct to use the normal distribution to compute the probability in part b? Why or why not?