Lazurus Steel rporation produces iron rods that are supposed to be 36 inches long. The machine that makes these rods doess not produce each rod exactly 36 inches long. The lengths of the rods are normally distributed and vary slightly. It is known that when the machine is working properly, the mean length of the rods is 36 inches. The standard deviation of the lengths of all rods produced on this machine is always equal to 0.035 inch. The quality control department at the company takes a sample of 20 such rods every week, calculates the mean length of these rods, and tests the null hypothesis, u = 36 inches, against the alternative hypothesis, u + 36 inches. If the null hypothesis is rejected, the machine is stopped and adjusted. A recent sample of 20 rods produced a mean length of 36.015 inches. Calculate the p-value for this test of hypothesis. Based on this p-value, will the quality control inspector decide to stop the machine and adjust it if he chooses the maximum probability of a Type I error to be 0.025? Use the normal distribution table. Round your answer to four decimal places. p-value = i The machine adjustment.

Jennifer needs to estimate the average age of vets in Houston. The standard deviation of ages is 17 years. She wants the standard error of her mean to be 0.3 years. How many vets is she going to need to sample to get at least that kind of accuracy?(be sure to round up)

You recently took a statistics exam in a large class. The instructor tells the class that the scores were Normally distributed, with a mean of 72 (out of 100) and a standard deviation of 12 . Your score was 96 . You would like to know what proportion of students did better than you did. Unfortunately, your calculator batteries are dead and you must now rely on Normal tables. You need to find which of the following?   the area to the left of 2 the area to the right of 2 the area to the right of 96 the area to the left of 96

Please be sure answers are correct.