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The viscosity of a fluid can be measured in an experiment by dropping a small ball into a calibrated tube containing the fluid and observing the random variable X, the time it takes for the ball to drop the measured distance. Assume that X is normally distributed with the mean of 20 seconds and a standard deviation of 0.5 second for a particular type of liquid.
(a) What is the standard deviation of the average time of 40 experiments?
(b) What is the probability that the average time of 40 experiments will exceed 20.1 seconds?
(c) Suppose the experiment is repeated only 20 times. What is the probability that the average value of X will exceed 20.1 seconds?
(d) Is the probability computed in part (b) greater or less than the probability computed in part (c)? Explain why this inequality occurs
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