Answer :
Answer:
The probability that exactly 6 transactions will be made at an ATM in the next 20 minutes = 0.06306 = 0.0631 to 4d.p
Step-by-step explanation:
This is a Poisson distribution problem
The Poisson distribution formula is given as
P(X = x) = (e^-λ)(λˣ)/x!
where λ = mean = 10 transactions per 20 minutes
x = variable whose probability is required = 6 transactions in the next 20 minutes
P(X = 6) = (e⁻¹⁰)(10⁶)/6! = 0.06306
The probability that exactly 6 transactions will be made at an ATM in the next 20 minutes is 0.0630.
What is the Poisson distribution?
A Poisson distribution is a probability distribution that is used to show how many times an event is likely to occur over a specified period.
The formula for Poisson distribution is given as,
[tex]P(X) = \dfrac{e^{-\lambda}\times \lambda ^ {x}}{x!}[/tex]
Given that 10 transactions were made in 20 minutes. We need to find the probability for 6 transactions in 20 minutes. So,
[tex]\lambda = 10[/tex] and [tex]x = 6[/tex]
The probability is,
[tex]P(X) = \dfrac{e^{-10}\times 10^6}{6!}[/tex]
[tex]P(X) = \dfrac { 45.399}{720}[/tex]
[tex]P(X) = 0.0630[/tex]
Hence we can conclude that the probability that exactly 6 transactions will be made at an ATM in the next 20 minutes is 0.0630.
To know more about Poisson Distribution, follow the link given below.
https://brainly.com/question/5673802.