Question

On the average, 1.6 customers per minute arrive at any one of the checkout counters of Sunshine food market. What type of probability distribution can be used to find out the probability that there will be no customers arriving at a checkout counter in 10 minutes

Answer 1

Answer:

Poisson distribution

Step-by-step explanation:

Poisson distribution:

A discrete random variable X having the enumerable set {0,1,2,....} as the spectrum, is said to have Poisson distribution with parameter $\mu$ (>0), if the p.m.f given by

$P(X=x)=\frac{e^{-\mu}\mu^x}{x!}$

               $=\frac{e^{-\lambda t}(\lambda t)^x}{x!}$

$\lambda$ = Average number of customer per minute= 1.6

t= time = 10 minutes

$\lambda t$= (1.6×10)=16

x= No customer arriving=0

$P(X=0)=\frac{e^{-16}(16)^0}{0!}$

               =$1.13\times 10^{-7}$

The probability that no customer arriving at a checkout counter for 10 minutes is $1.13\times 10^{-7}$.