Manufacturing and Product Development
Violin bows are made from various woods to accommodate musicians' preferences and demands. Some commonly used woods include snakewood, ironwood, hakia, and pernambuco. While the bows are carefully handcrafted, they vary slightly in weight. Suppose a bowmaker claims the weight of his bows is normally distributed with mean 60 grams and standard deviation 3.2 grams.
a. What is the probability that the weight of a randomly selected ironwood bow is between 58 and 62 grams?
b. Good musicians can detect an unacceptable bow weight, i.e., a weight that differs from the mean by more than two standard deviations. What is the probability that a bow weight is unacceptable?
c. Any manufactured bow that weighs more than 66 grams is reworked in order to decrease the weight. What is the probability that a randomly selected ironwood bow will need rework?
d. Suppose the weight of a randomly selected bow is 55 grams. Is there any evidence to suggest the mean weight is less than 60 grams? Justify your answer.