Answer to Question #281033 in Statistics and Probability for aparajita mishra

Question

A student has committed the errors which follows the Poisson distribution

with an average rate of 1.5 errors per class.

i) What is the probability that she makes at least 3 errors during one class?

ii) What is the probability that she has committed two ‘error-free’ classes in

the two weeks?

Answer 1

Let $X$ be a random variable representing the errors committed by the student. $X$ therefore follows a Poisson distribution with rate $\lambda=1.5$ per class.

$i)$

The probability that she makes at least 3 errors during one class is given as,

$p(X\ge 3)=1-p(X\lt3)=1-\{p(X=0)+p(X=1)+p(X=2)\}$

$=1-\{0.2231+0.335+0.2510\}=1-0.8090=0.1912$

Therefore, the probability that she makes at least 3 errors during one class is 0.1912.

$ii)$

In two classes, the rate $\lambda=1.5\times2=3$. Thus, the probability that she has committed two ‘error-free’ classes is given by,

$p(X=0)={e^3\times3^0\over0!}=e^3=0.0498$

Therefore, the probability that she has committed two ‘error-free’ classes is 0.0498.