) A certain
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
1) A certain protein is present in everyones saliva, but Covid 19 increases its concentration. An instant test is develeped based on this measuring this protein:
For people without covid 19, the protein has a concentration with a mean of 9 units/ml, and a standard deviation of 2 units/ml. For people with covid 19 the protein has a concentration 23 units/ml and standard deviation of 1 unit/ml
Suppose we set a cutoff value of the test at 19 units/ml. So above 19 units/ml they are considered to have covid 19, and below 19 units they are not.
i) Using Tchebychev's rule
a) What is the maximum probability of falsely labelling a healthy person as having covid 19? *(show work on all problems)
b) What is the maximum probability of incorrectly saying a person does not covid 19 when they do?
ii) Assume Tchebychev's rule is exact, calculate the probability of having Covid 19 if the test says you have it if
a) The background percentage of people with active covid 19 is .01
b) The background percentage of people with active covid 19 is .05
c)The background percentage of people with active covid 19 is .3
iii)Assume Tchebychev's rule is exact, calculate the probability of having Covid 19 if the test says you dont have it if
a) The background percentage of people with active covid 19 is .01
b) The background percentage of people with active covid 19 is .05
c)The background percentage of people with active covid 19 is .3
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