Let X be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood). The distribution of X for a healthy person is normally distributed with men u = 85 and standard deviation o = 25. A person suffers from severe excess in insulin would have a lower level of glucose. A blood test with result of X < 40 would be used as an indicator that medication is needed. (a) What is the probability that a healthy person will be suggested with medication after a single test? (b) A doctor uses the average result of 2 tests for diagnosis, that is X. The second test will be conducted one week after the first test, so that the two test results are independent. For many healthy persons, each has finished two tests, find the expectation and standard error of the distribution of X. (c) The doctor suggests medication will be given only when the average level of glucoses in the 2 blood tests is less than 40, that is X < 40, so to reduce the chance of unnecessary use of medication on a healthy person. Use the distribution in part (b)) to find the probability that a healthy person will be suggested with medication after 2 tests to verify this doctor's theory.
Let X be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood). The distribution of X for a healthy person is
(a) What is the
(b) A doctor uses the average result of 2 tests for diagnosis, that is X. The second test will be conducted one week after the first test, so that the two test results are independent. For many healthy persons, each has finished two tests, find the expectation and standard error of the distribution of X.
(c) The doctor suggests medication will be given only when the average level of glucoses in the 2 blood tests is less than 40, that is X < 40, so to reduce the chance of unnecessary use of medication on a healthy person. Use the distribution in part (b)) to find the probability that a healthy person will be suggested with medication after 2 tests to verify this doctor's theory.
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