Car security alarms go off at a mean rate of 3.8 per hour in a large Costco parking lot. Find the probability that in an hour there will be (Round your answers to 4 decimal places.) Probability (a) no alarms (b) fewer than four alarms (c) more than five alarms

a) 0.0224

b) 0.4735

c) 0.1844

Step-by-step explanation:

We use the Poisson probability distribution to solve this problem.

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 time interval.

In this problem, we have that:

(a) no alarms

(b) fewer than four alarms

(c) more than five alarms

Either there are five or fewer alarms, or there are more than five. The sum of the probabilities of these events is decimal 1. So

We want to find . So

In which

So

Then

2,600 divided by 80 = 32.5

step-by-step explanation:

1,645,493,059.35

step-by-step explanation: