## What is the probability that 8 cars arrive in three seconds?

1.    The number of hits on a certain website follows a Poisson distribution with a mean rate of 4 per minute.

a.   What is the probability that 5 hits are received in a given minute?

b.  What is the probability that 9 hits are received in 1.5 minutes?

c.    What is the probability that fewer than 3 hits are received in a period of 30 seconds?

2.   The number of cars arriving at a given intersection follows a Poisson distribution with a mean rate of 4 per second.

a.  What is the probability that 3 cars arrive in a given second?

b.   What is the probability that 8 cars arrive in three seconds?

c.    What is the probability that more than 3 cars arrive in a period of two seconds?

3.   A random variable X has a binomial distribution, and a random variable Y has a Poisson distribution. Both X and Y have means equal to 3. Is it possible to determine which random variable has the larger variance? Choose one of the following answers:

a.  Yes, X has the larger variance.

b.  Yes, Y has the larger variance.

c.   No, we need to know the number of trials, n, for X.

d.  No, we need to know the success probability, p, for X.

e.  No, we need to know the value of λ for Y

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