On a particularly busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeding drivers. Assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes.
(a) Calculate the rate parameter λ.
(b) What is the probability of a waiting time less than 10 minutes between successive speeders?
(c) What is the probability of a waiting time in excess of 25 minutes between successive speeders?

a)

b) 48.62% probability of a waiting time less than 10 minutes between successive speeders

c) 18.92% probability of a waiting time in excess of 25 minutes between successive speeders

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

In which is the decay parameter.

The probability that x is lower or equal to a is given by:

Which has the following solution:

(a) Calculate the rate parameter λ.

Mean of 15 minutes. So

(b) What is the probability of a waiting time less than 10 minutes between successive speeders?

48.62% probability of a waiting time less than 10 minutes between successive speeders

(c) What is the probability of a waiting time in excess of 25 minutes between successive speeders?

Either the waiting time is 25 or less, or it is in excess of 25 minutes. The sum of the probabilities of these events is decimal 1. So

We want P(X > 25). So

18.92% probability of a waiting time in excess of 25 minutes between successive speeders

nothjing

step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet