Weights of pennies. The distribution of weights of United States pennies is approximately normal with a mean of 2.5 grams and a standard deviation of 0.03 grams.
(a) What is the probability that a randomly chosen penny weighs less than 2.4 grams?
(b) Describe the sampling distribution of the mean weight of 10 randomly chosen pennies.
(c) What is the probability that the mean weight of 10 pennies is less than 2.4 grams?
(d) Sketch the two distributions (population and sampling) on the same scale.
(e) Could you estimate the probabilities from (a) and (c) if the weights of pennies had a skewed distribution?