probability exponential distribution

[Billy]

The time between shots at goal in a football (soccer) game, X, has an exponential distribution with a mean of 9 shots every twenty minutes. Determine the following:

(a) What is the probability of the time between shots being greater than 5 minutes?
(b) What is the probability of more than 20 shots in 40 minutes?
(c) In 6 non-overlapping 5 minute intervals, what is the probability of at least one 5 minute period with no shots at goal?

please help! many thanks in advanced

 

[tkhunny]

Please show your basic understanding of the exponential distribution, probably gleaned from your course materials or class discussion. Please do not ever type in a problem with no work shown. Give us a clue where you are! You CAN'T be NOWHERE. I just don't believe that.

 

[Billy]

would a) be:

P(X>5)= 1 - P(X<= 5)
1 - F(5)
1-(1-e^-20(5)/9)
= 0.0000149453

this doesnt seem right to me because it is so very small

is this the corret solution?

 

[tkhunny]

Let's play like it's a Normal Distribution

20/9 = 2.22222

5/2.22222 = 2.25ish

One might expect 2-3% of the distribution higher than that for a Normal. The exponential is packed to the left, so I'm feeling a little better about it.

You are right. It does seem rather small. That doesn't amke it wrong. Check your arithmetic and see if you can convince yourself one way or the other.