Question

A drug is accurate 97% of the time. If the test is given to 2000 people who have not taken drugs, what is the probablity that at least 62 will test positive?

Answer #1

For 2000 people who have not taken drugs, number of people who will test positive can be modelled here as:

This can be approximated to a normal distribution as:

The required probability here is computed as:

Applying the continuity correction, we get here:

Converting this to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

**Therefore 0.4221 is the required probability
here.**

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First, use the normal approximation to the binomial, and use the
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Normal Approximate Probability = ?
Now use the binomial distribution.
Exact Binomial Probability = ?
Does the normal distribution make a pretty good approximation to
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No, those probabilities are far...

A drug test is accurate 91% of the time. If the test is given to
225 people who have not taken drugs, what is the probability that
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First, use the normal approximation to the binomial, and use the
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Now use the binomial distribution.
Exact Binomial Probability = ?
Does the normal distribution make a pretty good approximation to
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Yes, that looks pretty good....

Acme Manufacturing Company requires all
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How many of Acme’s employees use drugs?
How many of the employees who use drugs get a positive test
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Of the employees who get a positive test result,...

Suppose we assume that 5% of people are drug users. If a person
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Test shows drug use
Test shows no drug use
Total
Subject uses drugs
90
4,995
5,085
Subject does not use drugs
10
94,905
94,915
Total
100
99,900
100,000
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