Many backyard gardeners prefer Silver Queen Hybrid corn. This late-season variety is very sweet and has tender, white kernels. In some locations in the Northeast, gardeners have trouble harvesting this variety because of its longer growing time. The temperature of the soil should be at least 65°F before planting, and the growing time is approximately normal with mean 92 days and standard deviation 5 days.
a. What is the probability that a randomly selected seed will mature in less than 90 days?
b. What is the probability that a randomly selected seed will mature in between 95 and 100 days?
c. Suppose a row in a backyard garden contains 12 plants. What is the probability that four will be ready for dinner by the 95th day?
d. Find a value h such that 99% of all plants are ready to be harvested within h days.
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.