Question A part 1 A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the probability that the disease will be detected by the test is 0.9. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 3% of the population who take this test have the disease. , (Round your answers to three decimal places.) 1: If the test administered to an individual is positive, what is the probability that the person has the disease? 2: If an individual takes the test twice and the test is positive both times, what is the probability that the person has the disease? (Assume that the tests are independent.) Question A part 2 In a survey of 1000 eligible voters selected at random, it was found that 200 had a college degree. Additionally, it was found that 90% of those who had a college degree voted in the last presidential election, whereas 45% of the people who did not have a college degree voted in the last presidential election. Assuming that the poll is representative of all eligible voters, find the probability that an eligible voter selected at random will have the following characteristics. (Round your answers to three decimal places.) 1: The voter had a college degree and voted in the last presidential election. 2: The voter did not have a college degree and did not vote in the last presidential election. 3: The voter voted in the last presidential election. 4: The voter did not vote in the last presidential election. Question A part 2 For the demand equation below, x represents the quantity demanded in units of 1000 and p is the unit price in dollars. 9p + 8x − 360 = 0; p = 5 1: Determine the quantity demanded corresponding to the given unit price p = Question A part 3 In 2016, National Textile installed a new textile machine in one of its factories at a cost of $250,000. The machine is depreciated linearly over 10 years with a scrap value of $10,000. 1: Find an expression for the textile machine's book value in the t the year of use (0 ≤ t ≤ 10). 2: Find the machine's book value in 2024. $ 3: Find the rate at which the machine is being depreciated. $ per year Question A part 4 The demand equation for the Wilkinson washable computer keyboard is p = −0.02x + 60 where x is the quantity demanded per month and p is the unit price in dollars. 1: What is the highest price (theoretically) anyone would pay for a washable keyboard? $ 2: What is the quantity demanded per month when the unit price is $20? units per month Question B part 1 The demand equation for the Sicard sports watch is p = −0.035x + 70 where x is the quantity demanded per week and p is the unit price in dollars. 1: What is the highest price (theoretically) anyone would pay for the watch? Question B part 2 For the supply equation below, x is the quantity supplied in units of 1000 and p is the unit price in dollars. p = 1/2x + 30; p = 36 1: Determine the number of units of the commodity the supplier will make available in the market at the given unit price. Question B part 3 A manufacturer has a monthly fixed cost of $28,500 and a production cost of $8 for each unit produced. The product sells for $11/unit. (a) What is the cost function? C(x)= (b) What is the revenue function? R(x)= (c) What is the profit function? P(x)= (d) Compute the profit (loss) corresponding to production levels of 8,000 and 11,000 units. P(8,000)= P(11,000)= Question B part 3 An office building worth $1 million when completed in 2010 is being depreciated linearly over 50 years. What was the book value of the building in 2014? What will it be in 2025? (Assume the scrap value is $0.) Bv in 2014= Bv in 2025= Question B part 4 An automobile purchased for use by the manager of a firm at a price of $31,500 is to be depreciated by using the straight-line method over 5 years. 1:What will be the book value of the automobile at the end of 3 years? (the scrap value is $0.) Question C part 1 A certain economy's consumption function is given by the equation C(x) = 0.75x + 8 where C(x) is the personal consumption expenditure in billions of dollars, and x is the disposable personal income in billions of dollars. Find C(0), C(50), and C(100). C(0) = billion dollars C(50) = billion dollars C(100) = billion dollars Question C part 2 Auto Time, a manufacturer of electronic digital timers, has a monthly fixed cost of $47,000 and a production cost of $8 for each timer manufactured. The timers sell for $15 each. (a) What is the cost function C(x)? C(x) = (b) What is the revenue function R(x)? R(x) = (c) What is the profit function P(x)? P(x) =
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question A part 1
A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the
1: If the test administered to an individual is positive, what is the probability that the person has the disease?
2: If an individual takes the test twice and the test is positive both times, what is the probability that the person has the disease? (Assume that the tests are independent.)
Question A part 2
In a survey of 1000 eligible voters selected at random, it was found that 200 had a college degree. Additionally, it was found that 90% of those who had a college degree voted in the last presidential election, whereas 45% of the people who did not have a college degree voted in the last presidential election. Assuming that the poll is representative of all eligible voters, find the probability that an eligible voter selected at random will have the following characteristics. (Round your answers to three decimal places.)
1: The voter had a college degree and voted in the last presidential election.
2: The voter did not have a college degree and did not vote in the last presidential election.
3: The voter voted in the last presidential election.
4: The voter did not vote in the last presidential election.
Question A part 2
For the demand equation below, x represents the quantity demanded in units of 1000 and p is the unit price in dollars.
9p + 8x − 360 = 0; p = 5 1: Determine the quantity demanded corresponding to the given unit price p =
Question A part 3
In 2016, National Textile installed a new textile machine in one of its factories at a cost of $250,000. The machine is depreciated linearly over 10 years with a scrap value of $10,000.
1: Find an expression for the textile machine's book value in the t the year of use (0 ≤ t ≤ 10).
2: Find the machine's book value in 2024. $
3: Find the rate at which the machine is being depreciated. $ per year
Question A part 4
The demand equation for the Wilkinson washable computer keyboard is p = −0.02x + 60
where x is the quantity demanded per month and p is the unit price in dollars.
1: What is the highest price (theoretically) anyone would pay for a washable keyboard? $
2: What is the quantity demanded per month when the unit price is $20? units per month
Question B part 1
The demand equation for the Sicard sports watch is p = −0.035x + 70 where x is the quantity demanded per week and p is the unit price in dollars. 1: What is the highest price (theoretically) anyone would pay for the watch?
Question B part 2
For the supply equation below, x is the quantity supplied in units of 1000 and p is the unit price in dollars. p = 1/2x + 30; p = 36
1: Determine the number of units of the commodity the supplier will make available in the market at the given unit price.
Question B part 3
A manufacturer has a monthly fixed cost of $28,500 and a production cost of $8 for each unit produced. The product sells for $11/unit.
(a) What is the cost
(b) What is the revenue function? R(x)=
(c) What is the profit function? P(x)=
(d) Compute the profit (loss) corresponding to production levels of 8,000 and 11,000 units.
P(8,000)=
P(11,000)=
Question B part 3
An office building worth $1 million when completed in 2010 is being depreciated linearly over 50 years. What was the book value of the building in 2014? What will it be in 2025? (Assume the scrap value is $0.)
Bv in 2014=
Bv in 2025=
Question B part 4
An automobile purchased for use by the manager of a firm at a price of $31,500 is to be depreciated by using the straight-line method over 5 years. 1:What will be the book value of the automobile at the end of 3 years? (the scrap value is $0.)
Question C part 1
A certain economy's consumption function is given by the equation C(x) = 0.75x + 8
where C(x) is the personal consumption expenditure in billions of dollars, and x is the disposable personal income in billions of dollars. Find C(0), C(50), and C(100).
C(0) = billion dollars
C(50) = billion dollars
C(100) = billion dollars
Question C part 2
Auto Time, a manufacturer of electronic digital timers, has a monthly fixed cost of $47,000 and a production cost of $8 for each timer manufactured. The timers sell for $15 each.
(a) What is the cost function C(x)? C(x) =
(b) What is the revenue function R(x)? R(x) =
(c) What is the profit function P(x)? P(x) =
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