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
[tex]\mu=2.2[/tex]
Since, this is poisson's distribution
so, we can use formula
[tex]f(t)=\frac{\mu^te^{-\mu}}{t!}[/tex]
now, we have to find
the probability that the cashier will total between four and ten trays in a minute
we can plug [tex]\mu=2.2[/tex]
[tex]f(t)=\frac{(2.2)^te^{-2.2}}{t!}[/tex]
At t=5:
[tex]f(5)=\frac{(2.2)^5e^{-2.2}}{5!}[/tex]
[tex]f(5)=0.04759[/tex]
At t=6:
[tex]f(6)=\frac{(2.2)^6e^{-2.2}}{6!}[/tex]
[tex]f(6)=0.01745[/tex]
At t=7:
[tex]f(7)=\frac{(2.2)^7e^{-2.2}}{7!}[/tex]
[tex]f(7)=0.00548[/tex]
At t=8:
[tex]f(8)=\frac{(2.2)^8e^{-2.2}}{8!}[/tex]
[tex]f(8)=0.00151[/tex]
At t=9:
[tex]f(9)=\frac{(2.2)^9e^{-2.2}}{9!}[/tex]
[tex]f(9)=0.00037[/tex]
[tex]P(4<t<10)=P(5)+P(6)+P(7)+P(8)+P(9)[/tex]
[tex]P(4<t<10)=0.04759+0.01745+0.00548+0.00151+0.00037[/tex]
[tex]P(4<t<10)=0.0724[/tex]
