Question

A cashier at carter's cafeteria can total an average of 2.2 trays per minute. the probability that the cashier will total between four and ten trays in a minute is:

Answer 1

A cashier at Carter's cafeteria can total an average of 2.2 trays per minute. the probability that the cashier will total between four and ten trays in a minute is: 0.1082

Answer 2

The probability that the cashier will total between four and ten trays in a minute is 0.0724

Explanation:

We are given

A cashier at carter's cafeteria can total an average of 2.2 trays per minute

so, mean =2.2

`\mu=2.2`

Since, this is poisson's distribution

so, we can use formula

`f(t)=(\mu^te^(-\mu))/(t!)`

now, we have to find

the probability that the cashier will total between four and ten trays in a minute

we can plug
`\mu=2.2`

`f(t)=((2.2)^te^(-2.2))/(t!)`

At t=5:

`f(5)=((2.2)^5e^(-2.2))/(5!)`

`f(5)=0.04759`

At t=6:

`f(6)=((2.2)^6e^(-2.2))/(6!)`

`f(6)=0.01745`

At t=7:

`f(7)=((2.2)^7e^(-2.2))/(7!)`

`f(7)=0.00548`

At t=8:

`f(8)=((2.2)^8e^(-2.2))/(8!)`

`f(8)=0.00151`

At t=9:

`f(9)=((2.2)^9e^(-2.2))/(9!)`

`f(9)=0.00037`

`P(4<t<10)=P(5)+P(6)+P(7)+P(8)+P(9)`

`P(4<t<10)=0.04759+0.01745+0.00548+0.00151+0.00037`

`P(4<t<10)=0.0724`