The distribution of customers arriving at a bank is Poisson with a standard deviation of 2 customers per 15-minutes. What is the probability that more than 3 customers arrive during 15 minutes

56.65% probability that more than 3 customers arrive during 15 minutes

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given interval, which is the same as the variance. The standard deviation is the square root of the variance.

Standard deviation of 2 customers per 15-minutes.

So

What is the probability that more than 3 customers arrive during 15 minutes

Either three or less customers arrive, or more than 3 do. The sum of these probabilities is decimal 1. Mathematically, we have that:

We want P(X > 3). So

In which

56.65% probability that more than 3 customers arrive during 15 minutes

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.