The number of customers at Winkies Donuts between 8:00 A. M. and 9:00 A. M. is believed to follow a Poisson distribution with a mean of 2 customers per minute. a . During a randomly selected one-minute interval during this time frame, what is the probability of 6 customers arriving to Winkies? b. What is the probability at least 2 minutes elapse between customer arrivals?

a) 0.012 or 1.2% probability

b) 0.2817 or 28.17%

Step-by-step explanation:

a) In this case, we will apply Poisson distribution because of the given period of time as distribution.

We use the Poisson distribution formula:

Where;

X= Random variable (number of customers arriving in the interval)

u= mean

Applying the formula we have;

Therefore, there is a 0.012 probability of 6 customers arriving in a randomly selected 1 minute interval.

b) Here, we use exponential problem formula

= 1 - 0.71828 = 0.28172

Therefore, there is a probability of 0.28172 of 2 minutes gap