Let x be a random variable with the following probability distribution: Value x of X......P(X = x) ........-1...............0.05 .........0...............0.05 .........1...............0.60 .........2...............0.05 .........3...............0.15 .........4...............0.10 Find the expectation E(X) an
Suppose that a certain college class contains 59 students. Of these, 35 are seniors, 30 are business majors, and 12 are neither. A student is selected at random from the class. a. What is the probability that the student is both a senior and a business major? b. Suppose that we are given the additional information that the s
Please help with the following problems. Provide step by step calculations. At a certain college, 51% of the students are female and 17% of the students major in civil engineering. Furthermore, 10% of the students both are female and major in civil engineering. a. What is the probability that a randomly selected female stu
This is for Quality Control Consider the xbar chart for the piston-ring example as follows, let ring diameter be normally distributed, and the sample size is n = 5. a) Find the two-sigma control limits for this chart. b) Suppose it was suggested that the two-sigma limits be used instead of the typical three-sigma limits.
Please see the attached file for full problem description.
Please see the attachment for the question. Let B and C be two events such that P(B) = 0.50 and P(C) = 0.05. a. Determine P(B U C), given that B and C are mutually exclusive. b. Determine P(B U C), given that B and C are independent.
Suppose that A and B are independent events such that P(A)=0.30 and P(B)=0.40. Find the following probabilities... (see attachment for full question)
The solution gives an intuitive approach to probability problems involving dice. The technique is illustrated by calculating probabilities for the game of "craps".
A popular dice game, called "craps," is played in the following manner. A player starts by rolling two dice. If the result is a 7 or 11, the player wins. If the result is 2, 3, or 12, the player loses. For any other sum appearing on the dice, the player continues to roll the dice until that outcome reoccurs (in which case th
Please see the attached file for full problem description with all proper "X" symbols. --- Can you show me how to complete this kind of problem? Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" ( ) and "boys" ( ), which we write , , etc. For ea
Problem 1 We know the IQ of people is normally distributed with mean 120 and standard deviation (SD) of 25. Calculate the probability that an adult will have a ) IQ less than 100 b) IQ greater than 150 c) IQ between 100 and 150 d) Any person with a score over 200 is considered a genius. In a population of 10000
Those who have quit smoking often return to the habit. The authors of a paper concluded that forbidding smoking in the smoker's residence was a significant predictor of the ability to abstain from smoking. They collected data, calculated statistics, and presented the following as support for their conclusion: OR=1.95 C.I.
PROBLEM 4 Out of 11 people applying for an assembly job, 3 cannot do the work. Suppose two persons will be hired. (a) How many distinct pairs are possible? (b) In how many of the pairs will 0 or 1 people not be able to do the work? (c) If two persons are chosen in a random manner, what is the probability that neither will b
PROBLEM 3 Items coming off a production line are categorized as good (G), slightly blemished (B), and defective (D), and the percentages are 80%, 15% and 5%, respectively. Suppose that two items will be randomly selected for inspection and the selections are independent. (a) List all outcomes and assign probabilities. (b) Fin
PROBLEM 1 PART ONE In a shipment of 15 room air conditioners, there are 3 with defective thermostats. Two air conditioners will be selected at random and inspected one after another. Find the probability that (a) The first is defective. (b) The first is defective and the second is good. (c) Both are defective. (d) The sec
Records of student patients at a dentist's office concerning fear of visiting the dentist suggest the following proportions: (see attachment for full question).
Suppose P(A)= 0.55, P (B)= 0.32 and P( ) = 0.20 (see attachment for full question)
What is the probability that an assembly will have exactly one defect? What is the probability that it contains one or more nonconformances? How many would have a tensile strength in excess of 48 lb? What fraction of these batteries would be expected to survive beyond 1000 days?
2-17 A mechatornic assembly is subjected to a final functional test. Suppose that defects occur at random in these assemblies, and that defects occur according to a Poisson distribution with parameter = 0.02 a) What is the probability that an assembly will have exactly one defect? b) What is the probability that an assemb
THE PROBLEM IS ATTACHED AS MICROSOFT WORD.
For two events A and B, the following probabilities are specified. P (A) = 0.52 P (B) = 0.36 P (AB) =0.20 (a) Enter these probabilities in the following table, See attached file for full problem description.
A sample space consists of 8 outcomes with the following probabilities. See attached file for full problem description.
A roulette wheel has 34 slots, 2 of which are green, 16 are red, and 16 are black. A successful bet on black or red doubles the money, whereas one on green fetches 30 times as much. If you play the game once by betting $2 on the black, what is the probability that: a) You will lose your $2? b) You will win $2?
Suppose you are eating at a pizza parlor with two friends. You have agreed to the following rule about who will pay the bill: Each person will toss a coin. The person who gets a result that is different from the other two will pay the bill. If all three tosses yield the same result, the bill will be shared by all. Find the proba
Develop a simulation model in EXCEL and use it to answer the following questions. 1. On average, how much revenue does Dr. Benson?s practice in laser surgery generate each week? (Use 500 replications.) 2. On average, how much revenue would the laser surgery generate each week if Dr. Benson did not cancel sessions with two or fewer reservations? 3. Dr. Benson believes that 40% of the people attending the information sessions would have the surgery if she reduced the price to $1,500. Under this scenario, how much revenue could Dr. Benson expect to realize per week from laser surgery?
Dr. Sarah Benson is an ophthalmologist who, in addition to prescribing glasses and contact lenses, performs optical laser surgery to correct nearsightedness. This surgery is fairly easy and inexpensive to perform. Thus, it represents a potential gold mine for her practice. To inform the public about this procedure, Dr. Benson ad
Let X1 and X2 be two independent standard normal random variables. Let Y1 = X1+X2 and Y2=X1/X2. a) Find the joint density of Y1 and Y2 b) Find the marginal density of Y1 and Y2 (The distribution of Y2 is known as the Cauchy distribution).
Suppose X1 and X2 are independent exponential (λ) random variables. Let Y1=X1-X2 and Y2=X2. a) Find the joint density of Y1 and Y2. b) Find the marginal density of Y1.
Suppose X and Y are independent chi-square random variables with m and n degrees of freedom respectively. Let U = (X/m) / (Y/n) a) Find the density of U (The distribution of U is called the F-Distribution with m and n degrees of freedom). b) Find the density of V = U / (1+U)
Let Z be a standard normal random variable and let V have a chi-square distribution with n-degrees of freedom. Assume that Z and V are independent and let T = Z / √ (V/n) Find the density of T (The distribution of T is known as the t-distribution with n degrees of freedom.)
Find the probability for the various situations
NewSource Inc. uses natural gas in its production-processing operations. Neighboring companies in its upstate Ohio area have successfully drilled for gas on their premises, and NewSource is considering following suit. Their initial expenditure would be drilling, which would cost $80,000. If they strike gas, they would have to
Our psychology department received a new statistics text for review. Prof. Smart in his review provided an interesting table of corrections. Type: Alterations: 20%, Spelling 50%, Spelling and alterations: 10%. Assuming that spelling and alterations are the only possible types of corrections, calculate the probability of spot