Question

4. Twelve percent of all army recruits are too short for parade duties at national cemeteries. The minimum height for this duty is 70 inches. If the distribution of recruits’ heights is normal with a standard deviation of 3 inches, what is the average recruit height? (6 pts)

5. Tuna cans filled by a certain machine should weigh, on average, 6.5 ounces with a standard deviation of 0.01 ounces. This is true if the machine is working properly. Past evidence demonstrates that the distribution of weights is normal.

a. Quality inspectors will accept all cans between 6.475 and 6.525 ounces. What proportion of the cans will pass this quality inspection? (6 pts)

b. Suppose the packing machine is mis-calibrated and fills cans with an average of 6.495 ounces. What is the probability that a can will pass inspection, based upon the inspector’s rule from part (a), even though the machine is not filling according to the label specifications?

Answer 1