Cars arriving for gasoline at a Shell station follow a Poisson distribution with a mean of 1010 per hour. (Enter all answers rounded to at least 3 decimal places.) (a) Determine the probability that over the next hour, only one car will arrive. (b) Compute the probability that in the next 3 hours, more than 29 cars will arrive.

a)

b) For this case the new parameter would be:

And we want to calculate the following probability:

And we can use the complement rule for this case:

And for this case we can use the following excel code in order to find the required probability:

"=1-POISSON.DIST(29,30,TRUE)"

And we got:

Step-by-step explanation:

Part a

Let X the random variable that represent the number of cars arriving for gasoline at Shell station. We know that

The probability mass function for the random variable is given by:

And for this case we want this probability:

Using the probability mass function we got:

Part b

For this case the new parameter would be:

And we want to calculate the following probability:

And we can use the complement rule for this case:

And for this case we can use the following excel code in order to find the required probability:

"=1-POISSON.DIST(29,30,TRUE)"

And we got:

Arithmetic,  nth =  a + (n - 1)d,   common difference, d = 5

a₁₂ = a + (12 -1)d = 63

a + 11d = 63

a + 11*5 = 63

a = 63 - 11*5

a = 63  - 55

a = 8

So the nth term = a + (n - 1)d = 8 + (n - 1)5

8 + 5*(n - 1)

8 + 5n - 5

8 - 5 + 5n

3 + 5n

So nth term = 3 + 5n