Question

Consider the probability that more than 99 out of 159 people have not been in a car accident. Assume the probability that a given person has not been in a car accident is 61%. Approximate the probability using the normal distribution.

Answer 1

The number of people who have not been in a car accident out of the 159 people here could be modelled as:

This can be approximated to a normal distribution here as:

The probability that more than 99 out of 159 people have not been in a car accident is computed here as:

P(X > 99)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.3719 is the required probability here.