A survey is taken among customers of a fast-food restaurant todetermine preference for hamburger or chicken. Of 200 respondentsselected, 75 were children and 125 were adults. 120 preferredhamburger and 80 preferred chickens. 55 of the children preferredhamburger and 20 preferred chickens. Set up a 2x2 contingency tableusing this information and answer the following questions:
Age/ Food | Hamburger | Chicken | Total |
Child | | | |
Adult | | | |
Total | | | 200 |
What is the probability that a randomly selected individual isan adult?
What is the probability that a randomly selected individual is achild and prefers chicken?
Given the person is a child, what is the probability that thischild prefers a
hamburger?
Assume we know that a person has ordered chicken, what is theprobability that this individual is an adult?
Are food preference and age statistically independent?
2) Three messenger services deliver to a small town in Oregon.Service A has 60% of all the scheduled deliveries, serviceB has 30%, and service C has the remaining 10%.Their on-time rates are 80%, 60%, and 40% respectively. Defineevent O as a service delivers a package on time.
Calculate P(A and O)
Calculate P(B and O)
Calculate P(C and O)
Calculate the probability that a package was delivered ontime.
If a package was delivered on time, what is the probability thatit was service A?
If a package was delivered 40 minutes late, what is theprobability that it was service A?
3) The number of power outages at a nuclear power plant has aPoisson distribution with a mean of 6 outages per year.
What is the probability that there will be exactly 3 poweroutages in a year?
What is the probability that there will be at least 1 poweroutage in a year?
What is the variance for this distribution?
What is the mean power outage for this nuclear power plant in adecade?
