1. An insurance company knows that in the entire population of millions of homeowners, the mean annual loss from fire is μ = $500 and the standard deviation of the loss is σ = $3000. The distribution of losses is strongly right skewed: most policies have $0 loss, but a few have large losses. If the company sells 10,000 policies, what is the probability that it can safely base its rates on the assumption that its average loss will be no greater than $515?
2. To estimate the mean heightμof male students on your campus, you will measure an SRS of students. Heights of people of the same sex and similar ages are close to Normal. You know from government data that the standard deviation of the heights of young men is about 2.8 inches. Suppose that (unknown to you) the mean height of all male students is 70 inches.
(a) If you choose one student at random, what is the probability that he is between 66 and 68 inches tall?
(b) You measure 25 students. What is the standard deviation of the sampling distribution of their average height x???
(c) What is the probability that the mean height of your sample is between 66 and 68 inches?
3.Sheila's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 miligrams per deciliter (mg/dl) one hour after having a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution withμ= 125 mg/dl andσ= 20 mg/dl.
(a) If a single glucose measurement is made, what is the probability that Sheila is diagnosed as having gestational diabetes?
(b) If measurements are made on 4 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes?
4. Sheila's measured glucose level one hour after a sugary drink varies according to the Normal distribution with μ = 125 mg/dl and σ= 20 mg/dl. What is the level L such that there is probability only 0.1 that the mean glucose level of 5 test results falls above L?