Question

1) The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with mean of three cracks every five miles. What is the probability that there are exactly two cracks that require repair in 3 miles of highway?

2) The volume of a shampoo filled into a container is a continuous random variable uniformly distributed with 240 and 260 milliliters. What is the probability that the container is filled with MORE THAN the advertised target of 255 milliliters?

3) The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. What is the probability that you wait between 10 and 20 minutes for a taxi?

Answer 1

Solution:

Question 1)

Given: The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with mean of three cracks every five miles. That is Mean = 3 per 5 miles then

rate= per mile

That is: X = The number of cracks in a section of interstate highway follows Poisson( ).

we have to find the probability that there are exactly two cracks that require repair in 3 miles of highway.

That is we have to find:

P( X = 2 ) = ........?

We have rate = 0.6 crack per miles ,then for three miles

rate = 3 X 0.6 = 1.8 cracks per three miles.

Thus X=Number of cracks per three miles follows Poisson distribution with parameter .

Use scientific calculator to find e^-1.8

e^-1.8 = 0.165299

Thus

Thus the probability that there are exactly two cracks that require repair in 3 miles of highway = 0.2678