Search & Filtering
The mean number of automobiles entering a mountain tunnel per two-minute period is one. An excessive number of cars entering the tunnel during a brief period of time produces a hazardous situation. Find the probability that the number of autos entering the tunnel during a two-minute period exceeds three. Does the Poisson model seem reasonable for this problem?
Probability distribution for a random variable x which corresponds to the number of pens that you have in your bag
(a) The random variable Y has a Poisson distribution and is such that P(Y = 0) = P(Y = 1). What is P(Y 2 = 1)?
(b) Cars arrive at a toll both according to a Poisson process with mean 80 cars per hour. If the attendant makes a one-minute phone call, what is the probability that at least 1 car arrives during the call?
Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. During a given hour, what are the probabilities that
(a) no more than three customers arrive?
(b) at least two customers arrive?
(c) exactly four customers arrive?
A salesperson has found that the probability of a sale on a single contact is approximately .03. If the salesperson contacts 100 prospects, what is the approximate probability of making at least one sale?
Let Y have a Poisson distribution with mean λ . Find E [Y (Y −1)] and then use this to show that Var(Y ) = λ
A corporation is sampling without replacement for n = 3 firms to determine the one from which to purchase certain supplies. The sample is to be selected from a pool of six firms, of which four are local and two are not local. Let Y denote the number of non-local firms among the three selected. Find:
(a) P(Y = 1)
(b) P(Y ≥ 1)
(c) P(Y ≤ 1)
A shipment of 20 cameras includes 3 that are defective. What is the minimum number of cameras that must be selected if we require that P(at least 1 defective)≥ .8?
In southern California, a growing number of individuals pursuing teaching credentials are choosing paid internships over traditional student teaching programs. A group of eight candidates for three local teaching positions consisted of five who had enrolled in paid internships and three who enrolled in traditional student teaching programs. All eight candidates appear to be equally qualified, so three are randomly selected to fill the open positions. Let Y be the number of internship trained candidates who are hired.
A warehouse contains ten printing machines, four of which are defective. A company selects five of the machines at random, thinking all are in working condition. What is the probability that all five of the machines are nondefective?
