The number of people arriving at a ballpark is random, with a Poisson distributed arrival. If the mean number of arrivals is 10, what is the probability (a) that there will be exactly 15 arrivals? (b) no more than 10 arrivals?

a) 3.47% probability that there will be exactly 15 arrivals.

b) 58.31% probability that there are no more than 10 arrivals.

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 time interval.

If the mean number of arrivals is 10

This means that

(a) that there will be exactly 15 arrivals?

This is P(X = 15). So

3.47% probability that there will be exactly 15 arrivals.

(b) no more than 10 arrivals?

This is

58.31% probability that there are no more than 10 arrivals.

- 1.613 = -1.6 or -1.61

-1.522 = -1.5 or -1.52

0.587 = 0.6 or 0.59

3.079 = 3.1 or 3.08

do you have the measurements?