Answer :
Answer:
The probability that no calls will occur during the next ten minutes is 0.0907.
Step-by-step explanation:
Poisson distribution:
Poisson distribution is a statistical distribution that helps to find out the number of events is likely occur in a specific time period.
[tex]P(X=x)=\frac{e^{-\lambda t}(\lambda t)^x}{x!}[/tex]
Given that,
Calls occur at an average rate of 1.2 every 5 minutes.
The average rate of call is [tex]\frac{1.2}{5}=0.24[/tex] per minute.
Here,
[tex]\lambda =0.24[/tex], t=10 and x=0
[tex]\therefore P(X=0)=\frac{e^{-0.24\times 10}(0.24\times 10)^0}{0!}[/tex]
=0.0907
The probability that no calls will occur during the next ten minutes is 0.0907.