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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.

Mixing the Constant with the Normal

Please see the attached file. There is a minor typo in the part(d). The function should be 1/(b-a), not 1/(a+b). From Conditional distribution and the Bivariate Normal distribution. Please show each step of your solution and check your final answer. Thank you.


From probability... Distributions of two random variables. The Correlation Coefficient. 1. A certain species of plant produces a flower that is either red, pink, white or on rare occasions blue. Form an analysis of the plants genes it is possible to calculate the the probability of a red flower is , the probability of white i

Employees in the textile industry can be segmented as follows.

4. Employees in the textile industry can be segmented as follows Employees Number Female and union 12,000 Female and nonunion 25,000 Male and union 21,000 Male and nonunion 42,000 a. Determine the probability of each event in this distribution. b. Are the events in this distribution mutually exclusive? Expl

Bernoulli Trial

15% of a city is self-employed. Find the probability that more than 3 of 6 of the people from this city sampled at random are self-employed.

Probability Problem Set (14 Questions)

1. During the last hour, a telemarketer dialed 20 numbers and reached 4 busy signals, 3 answering machines, and 13 people. Use this information to determine the empirical probability that the next call will be answered in person. 2. If you roll a die many times, what would you expect to be the relative frequency of rolling a

Probability Problem

Supose a pill exists with the property that one out of every 100 such pills contains a lethal amount of a substance, and that the other 99 are harmless. Caluclate how many people would be expected to die if 1,000 people each take 1 pill and if 1,000 people each take 10 pills. If 1,000 people take a single pill we would expect

The question is related to calculation of probability for different events from a sample of 2,000 licensed drivers revealed the following number of speeding violations. The second question is related to the selection students based on their gender and major.

I need some assistance with the attachment document. 8. A sample of 2,000 licensed drivers revealed the following number of speeding violations. Number of Violations Number of Drivers 0 1,910 1 46 2 18 3 12 4 9 5 or more 5 Total 2,000 a. What is the experiment? b. List one possible eve

Basic Probability Problems

Hello again! 1. Suppose you have 3 nickels, 2 dimes and 6 qtrs in your pocket. If you draw a coin ramdomly what is the probality that a. you will draw a dime ? b. you will draw a half dollar ? c. you will draw a qtr ? 2. you are rolling a pair of dice, one red and one green. what is the probability of the following outcomes

Probability Density Functions

From the Gamma, Chi-Square, and additional distributions. Please use any technological device available for you to solve the problem, but please explain each step of your solution. Thank you.

Waiting Lines and Queuing Theory Models

The problem is this: In planning for a major redesign, Beth collected data at her store on several consecutive Saturday mornings. She noticed that customers arrived at the checkout at a rate of approximately 100 per hour. Fully 20 percent of the customers had 10 items or less. Those people took about 2 minutes to serve on av

Future Value and Probability

Looking ahead to retirement , you sign up for automatic savings in a fixed income 401K plan to pay 6% per year compounded annually. You plan to invest $3500 at the each year for the next 20 years. How much will your account have in it at the end of 20 year? A spinner is used for which it is equally probable that the pointe


The probability of a coat having a defect is 1/3. What is the probability of there being 15 defective coats in a batch?

Probability - Waiting Time

Please see attached file for full problem description. Waiting Time 1) Let &#964; be a random variable which measures the time one has to wait for an event, such as default of a bond. As one can observe, the distribution of &#964; has the following density function: f(t) = ( &#955; > 0 is given ) a) Given any time