Reference no: EM13236707
1. A multiple-choice test has 6 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all questions randomly with a Probability of success = p =.25. Let X represent the number of correct answers out of six questions.
(i) Use binomial distribution to complete the table
(ii) Find the probability that the student will be successful in at least 4 questions.
(iii) Find the probability that the student will be successful in at most 3 problems
(iv) Compute the mean μ and the standard deviation σ for the above problem.
2. A bank recorded the number of ATM transactions made by its customers in one day. The number x of daily ATM transactions per customer can be approximated by the following probability distribution.
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x
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P(x)
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0
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.22
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1
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.28
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2
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.20
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3
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.12
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4
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.09
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5
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.07
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6
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.02
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Find (i) P(X≤4)
(v) P(2 < X ≤ 5)
(vi) Find the mean of X
(vii) Find the standard deviation of X.
3. A market research team compiled the following discrete probability distribution for families residing in Randolph County. In this distribution x represents the number of evenings the family dines outside their home during a week.
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x
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P(x)
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0
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0.30
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1
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0.50
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2
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0.10
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3
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0.10
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(i) Calculate the mean (Expected) number of dines outside their home.
(ii) Calculate the variance of the number of dines
(iii) Calculate the standard deviation of the number of dines
4. It is known that the number of business failure in USA per hour is distributed as Poisson with mean µ= 8 .
(i) Find the probability that exactly four businesses will fail in any given hour.
(ii) Find the probability that at least four businesses will fail in any given hour
(iii) Find the probability that more than four businesses will fail in any given hour.
5. On Saturdays, cars arrive at Sami Schmitt's Scrub and Shine Car Wash at the rate of 8 cars per twenty minute interval. Using the Poisson distribution,
(i) find the probability that five cars will arrive during the next five minute interval
(ii) Find the probability that at least three cars will arrive during the next 5 minute interval.
(iii) Find the probability that at no car will arrive during the next 5 minute interval.
6. A volunteer ambulance service handles zero to three service calls on any given day. The probability distribution for the number of service calls is as follows:
X: the number of service calls Probability
0 .15
1 .25
2 .40
3 .20
(i) What is the mean number of service calls per day
(ii) What is the variance of the number of service calls?
(iii) What is the standard deviation of the number of service calls?
(iv) Compute the coefficient of variation of the number of service calls.
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What is the change in clean springs profit-maximizing levels
: Suppose the Clean Springs Water Company has a monopoly on bottled water sales in California. If the price of tap water increases, what is the change in Clean Springs profit-maximizing levels of output, price, and profit
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Determine what is the new price and qauntity of gass
: Consider the market for gasoline. In the initial equilibrium, the price is $2.00 per gallon and the quantity is 100 million gallons. The price elasticity of demand is 0.70, and the price elasticity of supply is 1.0.
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Define ammonia can be made by reacting calcium cyanamide
: Ammonia can be made by reacting calcium cyanamide (CaCN2) with water as shown: CaCN2 + 3 H2O => CaCO3 + 2 NH3. How many grams of calcium cyanamide are required to react with 417.8 g of water
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Is the company allocating resources efficiently
: A survey performed by a major research organization indicated that businesses are wary of current economic conditions and are now restoring to electronic media, such as the Internet and the telephone, to transact business.
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Compute the coefficient of variation of the number
: What is the standard deviation of the number of service calls and compute the coefficient of variation of the number of service calls.
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Explain how many grams of water are required to react
: Ammonia can be made by reacting calcium cyanamide (CaCN2) with water as shown: CaCN2 + 3 H2O => CaCO3 + 2 NH3. How many grams of water are required to react with 212.9 g of calcium cyanamide
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What is the frequency of the oscillator
: A 2.00-m-long rope has a mass of 0.100 kg, What is the frequency of the oscillator if the power transmitted is 120 W
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Explain how many grams of alcl3 will be made
: Consider the reaction, 2 Al(s) + 3 Cl2(g) => 2 AlCl3(g). How many grams of AlCl3 will be made by the reaction of 7 moles of Al(s) with 27 moles of Cl2(g)
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Determine what is the annual growth rate
: U.S. Nominal GDP for the year 2010 was $14,658 billion, whereas in 2000 it was $9,951 billion. The GDP deflator for 2000 (2010) was 88 (111) using 2005 as a base year. Using the compound growth formula xt+n = xt(1 + g)^n
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