The number of customers arriving at a Post Office has an average of one person in one minute. Find the probability:
a. No customers arrive in one minute.
b. At least two customers arrive in four minutes.
c. Less than two customers in five minutes.
d. The mean and variance of the number of customers arriving in one hour.
At a certain busy junction, it is found that the number of accidents follows a Poisson distribution with a mean of two accidents per week. Find:
a. The probability that there is no accident in a week.
b. The probability that not more than two accidents happened in two weeks.
c. The value of k such that the probability that there are no accidents in k weeks is greater than 0.01.
1% of light bulbs produced at a factory are faulty. If a random sample of 250 light bulbs were taken, find the probability of getting three light bulbs faulty.
A factory packs biscuits in packets of 100. The probability that a biscuit is found to be broken is 0.002. Find the probability that a packet contains two broken biscuits.