Question

Let X denote the number of accidents that occur at a potato chips factory during a randomly selected week. If the mean of X is 3 , what is P(X=0) is equal to ? [A] 0.0789 [B] 0.3333 [C] 0.0498 [D] 0.037

Answer 1

The correct option is [C] P(X=0) = 0.498

Explanation:

Since the mean number of accidents is equal to 3 in a week,

We use the Poisson distribution to get the number of occurences,

`P(X = x) = m^xe^(-m)/x!\\Now,\\for \ x = 0,\\since \ m = mean = 3\\so,\\P(X = 0)=3^0e^(-3)/0!\\P(X=0)=e^(-3)\\P(X=0)=0.498`

P(X=0) = 0.498