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Waiting Line Models

The Sea View Resort uses a multiple-channel queue registration system. If the average service time is 9 minutes, there are three registration clerks, and guests arrive at the rate of one every 6 minutes, find a. Arrival and service rate. b. the probability all three clerks are idle. c. the probability a g

Probability distribution

1: A card is drawn and replaced 3 times from a 52-card deck. Find the probability that: A: 2 hearts were drawn b: at least 1 heart was drawn. 2: A box contains 3 red and 2 white marbles. A marble was drawn and replace 3 times. Find the probability that: A: 1 red was drawn 3: An unprepared student takes a 5-question tru

Operations management problems

Management Science 1. There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. Find the break-even point. 2. Administrators at a university are planning to offer a summer seminar. It costs $3000 to reserve

Probability-failure rate

A fire detection sensor is tested for its failure rate and found to have a mean failure rate of 3.6E-2 per hour of exposure with a standard deviation of .4E-2 per hour. The distribution of the failure rates is normal. If a sensor is selected at random from a large lot for installation in a system, what is the probability that it


A bin contains seven parts. The probability that any part in the bin is defective is 3.5E-3. If one part is selected at random from the bin, what is the probability that it is defective? Please explain equation used and steps to solve the problem.

Solve using venn diagrams

Solve using venn diagrams a and b are events in a sample space S such that P(A)=0.7,P(B)0.4 and P(A and B) = 0.2. a. draw a Venn diagram showing the overlapping sets A and B and fill in the probabilities of the four regions formed. b. find the probability that A occurs but B doesn not. c. find the probability that B occurs

Normal distribution

1) A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. Wha

Information about "Probabilities"

Can you answer these problems and show work. 1. How many variations in the first-, second-, and third-place finishes are possible in a 100-yd dash with 6 runners? 2. Suppose a family plans 6 children, and the probability that a particular child is a girl is ½. Find the probabilities that the 6-child family has at least

Find the probability when the system is idle.

Question: For an M/G/1 system with λ=20 and µ=35, σ=.005, find: 1) the probability when the system is idle. 2) the average length of the queue. 3) the average number in the system.

Finding the probability of repeats in finite sequences

1. What is the probability that out of 3 people, 2 were born in the same month. 2. What is the probability that a seven digit phone number has 1 or more repeats. 3. What is the probability that given 5 letters selected randomly from the alphabet, none is repeated? 4. What is the probability 2 of more randomly selected s

Probability Analysis : Roulette

1. Roulette is played at a table similar to the one in Figure 3.37. A wheel with the numbers 1 through 36 (evenly distributed with the colors red and black) and two green numbers 0 and 00 rotates in a shallow bowl with a curved wall. A small ball is spun on the inside of the wall and drops into a pocket corresponding to one of


See the attached file. 1. In determining automobile mileage ratings, it was found that the mpg in the city (X) for certain model is normally distributed, with a mean of 22.5 mpg and a standard deviation of 1.5 mpg. Find the following: a. P(X < 22.5) b. P(0 < X < 24) c. P(X > 25) d. P(22 < X < 22.5) e. P(X < 21) f. P(21


1. A survey of 100 MBA students found that 75 owned mutual funds, 45 owned stocks, and 25 owned both. a. What is the probability that a student owns a stock? A mutual fund? b. What is the probability that a student owns neither stocks nor mutual funds? c. What is the probability that a student owns either a stock or mutual f

Using the binomial distribution with order statistics

Let Y1<...<Y8 be the order statistics of 8 independent observations of a continuous type distribution with 70th percentile 27.3. a) Determine P(Y7<27.3) b) Find P(Y5<27.3<Y8) (See attachment for neater mathematical presentation of the question)


1. A cube has all 6 sides painted blue; this cube is then cut into 64 equal cubes. What is the probability, Pn where n = 1, 2, 3, that a little cube (one of the 64) picked at random will have n painted faces? 2. A person is given 4 coins each with equal and independent probabilities of being a nickel , a penny, a dime or


For #70a, b I know I have to use the complement like 1- (p(all four people with no good blood)) but do I multiply each probability or add them? For #66 not sure how begin this one For #63 I feel as if i don't have enough info to start with. For # 29,29b I get values that are way off the correct answers, like a) 13


In testing a new drug, researchers found that 5% of all patients using it will have a mild side effect. A random sample of 11 patients using the drug is selected. Find the probability that: a) exactly two will have this mild side effect b) at least one will have this mild side effect.