Question

Question 2      

The Wi-Fi signal is cut randomly at a constant rate of 17 times per day. What is the probability that the signal is cut more than 20 times in a random day?

1. Check if the conditions are met and use Normal approximation.
2. Use Excel to calculate the exact probability.
3. Calculate the error from the approximation.

Answer 1

Let X = The number of times the Wi-Fi signal is cut per day.

The rate of Wi-Fi signal is cut per day = = 17

Here X follows Poisson distribution.

So mean = = 17

a) If > 10 then we can use normal approximation to find the probability.

here = 17 > 10 so we can use normal approximation to find the probability.

Here we want to find P(X > 20) = 1 - P(X <= 20) ....( 1 )

Let's use continuity correction for getting better approximation.

P(X > 20) = 1 - P(X < 20+0.5 ) = 1 - P( X < 20.5) ....( 1 )

Let P( X < 20.5 ) = "=NORMDIST(20.5,17,SQRT(17),1)" = 0.802024

Plug this in equation ( 1 ), we get

P(X > 20) = 1 - 0.802024 = 0.197976

b)  Now let's find P(X > 20 ) using Poisson distribution

P( X > 20 ) = 1 - P( X <= 20) = "=1-POISSON(20,17,1)" = 0.194519

c) The error from the approximation = 0.197976 - 0.194519 = 0.003456

Note: Here we use excel commands to find the probabilities.

2) If is not too large then we need to use continuity correction for getting better approximation.