a. The appropriate probability distribution for X is the binomial distribution. This distribution satisfies the properties of a random variable X because it is a discrete probability distribution that models the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. In this case, the number of experiments is 5, and the probability of success is .1.
b. The probability that 4 machines will break down is 0.0010.
c. The probability that at least 4 machines will break down is 0.0062.
d. The expected number of machines that will break down in a day is 0.5.
e. The variance of the number of machines that will break down in a day is 0.4.
A manufacturing company has 5 identical machines that produce nails. The probability that a machine will break down on any given day is .1. Define a random variable X to be the number of machines that will break down in a day.
a. what is the appropriate probability distribution for X? Explain how X saisfies the properties of the distribution.
b. compute the probability that 4 machines will break down.
c. compute the probability that at least 4 machines will break down.
d. what is the expected umber of machines that will break down in a day?
e. What is the variance of the number of machines that will break down in a day?
1 answer
1 answer