Suppose it is known from large amounts of historical data that x, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete probability function: f(x) = e −6 6x x! , for x = 0, 1, 2, . .
(a) find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.
(b) find the probability that only 2 cars arrive

a) P(x>8) = 0.3937

b)  P(x = 2) =0.04661

Step-by-step explanation:

a) From to find the probabilty that in this specific time period, more than 8 cars arrive at the intesection, we use the probability function thus

P(x>8) = 1 - P(x≤8),  Cause you can use the complement for calculate this probability , then:

P(x≤8) = , until x= 8, then you obtain:

P(x≤8)=0.6063 and

P(x>8) = 1 - P(x≤8)= 1-0.6063 = 0.3937

b) P(x=2)=

 P(x = 2) =0.04661

Set it up as a ratio:

16 ounces feeds 80, 12 ounces feeds X

16 / 80 = 12 / X

Cross multiply:

16X = 80*12

16X = 960

Divide both sides by 16:

X = 960 / 16

X = 60

12 ounce feeder will feed 60 hummingbirds.