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.