Question

during class from 12pm - 3 pm, 30 questions are asked on average.

1- What is the standard deviation of the number of asked questions during the class?

2- What is the probability more than 10 questions are asked between 12:15 and 1:15 pm?

Answer 1

1.

Here, we use Poisson distribution with Mean = 30

Standard deviation of a Poisson random variable is :

2.

Here, in this case we use Exponential distribution as this is this case of inter-arrival distribution

Here we need to find the rate of questions in 1 hour (12.15 to 1.15 pm)

Since, 30 questions are asked in 3 hours (12-3 pm) , therefore 10 questions are asked per hour

So,

We need to find :

Probability that more than 10 questions are asked between 12:15 and 1:15 pm = P(X>10)

For exponential distribution , the CDF is :

So,

hence,

Probability that more than 10 questions are asked between 12:15 and 1:15 pm = 0.368