Question

In: Statistics and Probability

Consider the probability that more than 99 out of 159 people have not been in a...

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.

Solutions

Expert Solution

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.


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