SOLUTION: 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

Question 1192927: 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 μ = 85 and standard deviation σ = 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.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
a. z=(x-mean)/sd so z< (40-85)/25=-45/25 or -1.8
That probability is 0.0359
b. for two tests the expectation of the mean is still 85 mg%
The SE is the sd/sqrt(n) or 25/sqrt(2)=17.68
now z would b <-40/17.68=-2.26
That probability is 0.0119
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