The Northside Rifle team has two marksperson, Dick and Sally. Dick hits a bull's-eye 90% of the time, and Sally hits a bull's-eye 95% of the time. (a) What is the probability that either Dick or Sally or both will hit the bull's-eye if each takes one shot? (b) What is the probability that Dick and Sally with both hit the bull'
Ace Machine Works estimates that the probability its lathe tool is properly adjusted is 0.8. When the lathe is properly adjusted, there is a 0.9 probability that the parts produced pass inspection. If the lathe is out of adjustment, however, the probability of a good part being produced is only 0.2. A part randomly chosen is ins
I am a mature student (age 60) currently working for a training company. I have been asked to complete a training project which involves these questions and have already done some of the work; however, I need to confirm my answers for these last few questions. I have attached the questions along with the SMOG and FOG data she
Give a probability distribution for the following: In 1992, the Big 10 collegiate sports conference moved to have women compose at least 40% of its athletes within 5 years. Suppose they exactly achieve the 40% figure, and that 5 athletes are picked at random from Big 10 universities. The number of women is recorded. For th
7.5.3 Let X1, X2,..,Xn denote a random sample of size n from a distribution with pdf f(x; è) =èx^(è-1), 0<x<1, 0 elsewhere, and è>0. Show that the geometric mean (X1X2...Xn)^(1/n) of the sample is a complete sufficeint statistic for è. Find the maximum likelihood estimator and observe that it is a function of this geome
If a person adopts a pet there is a 45% it'll be a cat and 55% it will be a dog (a local dog and cat adoption). If a cat is adopted there is 60% chance it will be a female. If a dog is adopted there is 35% chance it is a female. A random selection is made and it was a male. What is the the probability that the selection is a
A) A fire station is to be located along a road of length A, A<∞. If fires will occur at points uniformly chosen of (0, A), where should the station be located so as to minimize the expected distance from the fire? That is, choose a so as to minimize E[|X-a|] when X is uniformly distributed over (0,A). b) N
6.3. Find the following probabilities for the standard normal random variable z: {see attachment} 6.7. Find a Zo that has area .9505 to its left. Find a Zo that has area .05 to its left.
If a particular batch of data is approximately normally distributed, we would find that approximately: a. 2 of every 3 observations would fall between ±1 standard deviation around the mean. b. 4 of every 5 observations would fall between ±1.28 standard deviations around the mean. c. 19 of every 20 observations would fall be
A professor grades homework by randomly choosing 5 out of 12 homework problems to grade. a) How many different groups of 5 are there from the 12 problems? b) Jerry did only 5 problems of one assignment. What is the probability that the problems he did comprised the group that was selected to be graded? c) Silvia did 7 pro
Sample Problems - Please show all your work. QUESTION 1 Suppose that you are working for an energy company that distributes natural gas to residents in a city. As the chief economic analyst, you are asked to analyze the demand for natural gas in your city. Let X denote the random monthly demand for natural gas in millions of
1) Records show that 30% of all patients admitted to a medical clinic fail to pay their bills and that eventually the bills are forgiven. Suppose n = 4 new patients represent a random selection from the large set of prospective patients served by the clinic. Find these probabilities: a) All the patients' bills will eventually h
Show all your work 1) If x has a binomial distribution with p = .5, will the shape of the probability distribution be symmetric, skewed to the left, or skewed to the right? Explain why. 2) A meteorologist in Chicago recorded the number of days of rain during a 30 day period. If the random variable x is defined as the numbe
1) A shipping company knows that the cost of delivering a small package within 24 hours is $14.80. The company charges $15.50 for shipment, but guarantees to refund the charge if delivery is not made within 24 hours. If the company fails to deliver only 2% of its packages within the 24 hour period, what is the expected gain per
The goal at U.S. airports handling international flights is to clear these flights within 45 minutes. Let's interpret this to mean that 95 percent of the flights are cleared in 45 minutes, so 5 percent of the flights take longer to clear. Let's also assume that the distribution is approximately normal. a) If the standard dev
Let X1 and X2 be two independent random variables having Poisson Dist. with parameters mew(subscript1)=2 and mew(subscript 2)=3 respectively. Then the marginal distribution for the random variable X2 is : a.) h(X2) = e^-2*2^Xz/X2!, x2=0,1,2,3,... b.) h(X2) = e^-5*5^Xz/X2!, x2=0,1,2,3,... c.) h(X2) = e^-3*3^Xz/X2!, x2
A lifespan in hours for an electrical component is a random variable x, with cumulative dist. funct.: F(x) = {1-e^-x/100 for x>0 0 elsewhere Determine probability function x for x: Which of the Following Answers: a.) F(x) = {100e^-x/100 for x>0 0 elsewhere b.) F(x) = {1-1/100
I.) The number of construction projects on a college campus follows Poissan's dist. with a mean=3. The probability that exactly two projects are currently taking place is: 1.) 0.4230 2.) 0.224 3.) 0.00 4.) 0.1990 J.) In an assembly line with robots, a particular component can be installed in 90 seconds if holes a
F.) A rock crushing company has 3 plants, all receiving blasted rock in bulk. The amount of rock that can be crushed by one of the plants in one day can be modeled by an exponential distribution. The mean amount of rocks that can be crushed per day by each plant is 4 tons. Assume plants operate independently of one another.
D.) Suppose X1 and X2 are independent exp. random variables, each with mean data and y=X1 and X2. What is the moment generating function for the random variable y? Which choice below is right: 1.) My = (1-t/beta)^-2 2.) My = (1-t/beta)^2 3.) My = (1-beta*t)^-2 4.) My = (1-beta*t)^2 E.) Let X1 and X2 be two di
Two separate questions below: A.) A bin contains 20 fuses of which 5 will be defective. If 2 fuses are selected at random without replacement, what is the probability that at most, one is defective?(Please show equation) B.) From a group of 5 men and 6 women, how many committees of size 3 are possible with 2 men and one w
If we choose a person at random from this database: i. What is the probability that this person will be female? ii. What is the probability that this person will be between 22 and 49 years old? iii. What is the probability that their overall job satisfaction is 4.7 or lower? b ) If we choose a person at random from this
Let X1, X2, X3 be random sample from a distribution of the continuous type having pdf f(x)=2x, 0 <x < infinity, 0 elsewhere. Compute the probability that the smallest of X1, X2, X3 exceeds the median of the distribution.
A fair coin is tossed 3 times. Let X be the number of heads on the third tossing and let Y be the total number of heads. Questions: a) Find the joint pdf of X and Y. b) Find the marginal pdf of X. Compute E(x) and V(x) - does X follow classical distribution? c) Find the marginal cdf of Y. Compute E(y) and V(y) - does Y
The density function of a continuous variable x is given by f(x) =x; 0≤x<1 and f(x) = 2-x; 1≤x<2 a) Find p(1/2≤x≤3/2) b) Find the median and quartiles of this distribution
A project involving the installation of a computer system comprises eight activities. The following table lists immediate predecessors and activity times (in weeks): {see attachment} 1) Draw a Project Network 2) What are the critical activities 3) What is the expected project completion time.
A manufacturer of computer printers claims that only 0.55% of all printers they produce fail out of the factory. As a computer store buyer, you purchase 150 of this company's printers. What is the chance that you get at least one defective printer out of this purchase? P(X is greater than or equal to 1)=____________ pleas
Assume that the number of Telephone calls arriving in an office during a 15 minute period has a Poisson distribution with mean number of calls equal 5. By using a Poisson Distribution Formula, find the Probability that during a 15minute period, there will be exactly 3 calls.
A jar contains marbles of different colors: 4 white, 6 black, 6 red, and 4 blue. On two random drawings, without replacement, find the probability that the first is black and the second is white. Assume that the draws are independent.
Take a deck of cards. A deeck has 52 cards with two major colors(Red and Black), with 26 cards each. Red colors comes in two shapes(heart and diamond), while black color shapes are called clubs and spades. Find the probability of obtaining Red or Queen. That is, find Probability(Red or Queen).