The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.6 years and a standard deviation of 0.6 years. He then randomly selects records on 40 laptops sold in the past. Round the answers of following questions to 4 decimal places. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the probability that one randomly selected laptop is replaced more than 3.7 years?

In a large section of a statistics​ class, the points for the final exam are normally​ distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top​ 10% receive​ A's, the next​ 20% received​ B's, the middle​ 40% receive​ C's, the next​ 20% receive​ D's, and the bottom​ 10% receive​ F's. Find the lowest score on the final exam that would qualify a student for an​ A, a​ B, a​ C, and a D. The lowest score that would qualify a student for an A is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a B is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a C is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a D is nothing. ​(Round up to the nearest integer as​ needed.)

The weights of 1,000 men in a certain town follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds.    From the data, we can conclude that the number of men weighing more than 165 pounds is about , and the number of men weighing less than 135 pounds is about .

Suppose that the hemoglobin levels among healthy females are normally distributed with a mean of 14.1 gdL. Research shows that exactly 95% of healthy females have a hemogoblin level of 16.1 gdL. What is the standard deviation of the distribution of hemoglobin levels and healthy females. Carry you intermediate computations to atleast four decimal places, and round your answer to at least two decimal places.