A commuter encounters four traffic lights each day on her way to work. Let X represent the number of these that are red lights. The probability mass function of X is as follows.

What is the probability that in a period of 100 days, the average number of red lights encountered is more than 2 per day?

Answer:

Step 1 of 1:

(a)

In this question, we are asked to find the probability that in a period of days, the average number of red lights encountered is more than per day.

A commuter encounters traffic lights each day.

Let represent the number of these that are red lights.

The probability mass function (PMF) of is as follows.

0 | 1 | 2 | 3 | 4 | |

0.1 | 0.3 | 0.3 | 0.2 | 0.1 |

when is a discrete random variable with probability mass function then we can write

= .The mean of is given by

= …………(1)

where the sum is for all possible values of .

The variance is given by the following formula

………….(2)

Hence mean number of red lights encountered per day will be

=

=

The standard deviation is