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

Answer:

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

Step-by-step 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

$f(t)=\frac{\mu^te^{-\mu}}{t!}$

now, we have to find

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

we can plug $\mu=2.2$

$f(t)=\frac{(2.2)^te^{-2.2}}{t!}$

At t=5:

$f(5)=\frac{(2.2)^5e^{-2.2}}{5!}$

$f(5)=0.04759$

At t=6:

$f(6)=\frac{(2.2)^6e^{-2.2}}{6!}$

$f(6)=0.01745$

At t=7:

$f(7)=\frac{(2.2)^7e^{-2.2}}{7!}$

$f(7)=0.00548$

At t=8:

$f(8)=\frac{(2.2)^8e^{-2.2}}{8!}$

$f(8)=0.00151$

At t=9:

$f(9)=\frac{(2.2)^9e^{-2.2}}{9!}$

$f(9)=0.00037$

$P(4$

$P(4$

$P(4$

Answer 2

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