MAC1105 Question 29 Section 6.2

Question

Cars arrive randomly at an intersection at an average rate of

100

cars per hour. The​ likelihood, or​ probability, that at least one car will enter the intersection within a period of x minutes can be estimated by

​P(x)=1−e−5x3.

a.	Find the likelihood that at least one car enters the intersection during a	2​-minute	period.
b.	Graphically determine the value of x that gives a​ 50-50 chance of at least one car entering the intersection during an interval of x minutes.

The likelihood that at least one car enters the intersection is about ____%

Answer 1

P(x) = 1 - e^(-5x/3)

(a) At x = 2 min

P(2)= 1-e^(-5(2)/3)

P(2) = 1 - (1/e^(10/3))

P(2) = 0.9643260067

Ans: 96%

(b) 50-50 chance

So, P(x) =1/2

P(x) = 1-e^(-5(x)/3)

1/2 = 1-e^(-5(x)/3)

ln(1/2) = ln(e^(-5(x)/3))

x = 3ln(2)/5

x = 0.416 mins

The likelyhood that at least one car enters the intersection is about 96%