4. If the price of one of the products associated with indifference curves increases, all else the same, what is the result? Prices will be lower, The individual is able to get to a lower level of utility. The individual is able to get to about the same level of utility. The individual is able to get to a higher level of utility.
5. If the price of one of the products associated with indifference curves decreases, all else the same, what is the result? Prices will be higher. The individual is able to get to about the same level of utility. The individual is able to get to a lower level of utility. The individual is able to get to a higher level of utility.
6. Which of the following statements best describes how individuals maximize their utility given a constraint? None of these possible answers make sense, This can be shown when the budget constraint is tangent to the lowest indifference curve possible, This can be shown when the budget constraint is tangent to the highest indifference curve well above the constraint, This can be shown when the budget constraint is tangent to the highest indifference curve
7. Whenever marginal benefit is less than marginal cost, the decision maker should do _____ of the activity. less, none, that exact amount, more
In: Economics
A manufacturer considering two alternative machine replacements. Machine 1 costs $1 million with an expected life of 5-years and will generate after-tax cash flows of $350,000 a year.
At the end of 5 years, the salvage value on Machine 1 is zero, but the company will be able to purchase another Machine 1 for a cost of $1.2 million.
The replacement Machine 1 will generate after-tax cash flows of $375,000 a year for another 5 years. At that time its salvage value will be zero.
The manufacturer's second option is to buy Machine 2 at a cost of $1.5 million today. Machine 2 will produce after-tax cash flows of $400,000 a year for 10 years, and after 10 years it will have after-tax salvage value of $100,000.
cost of capital for both machines is 12 percent.
In: Finance
Suppose a geyser has a mean time between eruptions of 79 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 20 minutes answer the following questions.
(a) What is the probability that a randomly selected time
interval between eruptions is longer than 88 ?minutes?
?(b) What is the probability that a random sample of 12 time intervals between eruptions has a mean longer than 88 ?minutes?
c) What is the probability that a random sample of 26 time intervals between eruptions has a mean longer than 88 minutes?
?(d) What effect does increasing the sample size have on the? probability? Provide an explanation for this result. Choose the correct answer below.
A.) The probability increases because the variability in the sample mean increases as the sample size increases.
B.) The probability decreases because the variability in the sample mean decreases as the sample size increases.
C.) The probability increases because the variability in the sample mean decreases as the sample size increases.
D.) The probability decreases because the variability in the sample mean increases as the sample size increases.
(e) What might you conclude if a random sample of 26 time intervals between eruptions has a mean longer than 88 ?minutes? Choose the best answer below.
A.) The population may be greater than 79.
B.) The population mean must be more than 79, since the probability is so low
C.) The population mean cannot be 79, since the probabilty is so low
D.) The population mean is 79 ?minutes, and this is an example of a typical sampling
In: Statistics and Probability
Problem 3: Rick goes to career fair booths in
the technology sector for data science jobs (e.g., Facebook,
Amazon, IBM, etc.). His likelihood of receiving an off-campus
interview invitation after a career fair booth visit depends on how
well he did in MIE 263. Especially, an A in MIE 263 results in a
probability p=0.95 of obtaining an invitation, whereas a C in MIE
263 results in a probability of p=0.15 of an invitation. (Whether a
student will get an invitation is independent on whether he will
get an invitation from other firms.) Furthermore, to get an A, a
student has to pass all quizzes. The probability that Rick passes
any quiz is 0.5. Rick’s performance on each
quiz is independent of his performance on all other quizzes.
c) Assuming that each student visits 5 booths during a typical
career fair, find the probability that an A student in MIE 263 will
not get an off-campus interview invitation.Similarly, find the
probability that a C student in MIE 263 will get an invitation
during a typical career fair.
d) Determine the probability that Rick will pass exactly two out of
the first four quizzes.
e) Determine the probability that the third quiz Rick takes is the
first one that he fails.
f) Given that Rick failed four times in his first eight quizzes,
determine the conditional
probability that his fifth failure will occur on the eleventh
quiz.
g) Determine the probability that Rick’s second failure occurs on
his fifth quiz.
In: Statistics and Probability
In a survey of U.S. adults with a sample size of 2040, 315 said Franklin Roosevelt was the best president since World War II. Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S. adults, complete parts (a) through (d).
(a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II.
The probability that both adults say Franklin Roosevelt was the best president since World War II =
(Round to three decimal places as needed.)
(b) Find the probability that neither adult says Franklin Roosevelt was the best president since World War II.
The probability that neither adult says Franklin Roosevelt was the best president since World War II =
(Round to three decimal places as needed.)
(c) Find the probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II.
The probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II =
(Round to three decimal places as needed.)
(d) Which of the events can be considered unusual? Explain. Select all that apply:
a.The event in part (b) is unusual because its probability is less than or equal to 0.05.
b.None of these events are unusual
c.The event in part (c) is unusual because its probability is less than or equal to 0.05.
d. The event in part (a) is unusual because its probability is less than or equal to 0.05.
In: Statistics and Probability
1. In a survey of U.S. adults with a sample size of 2004, 345 said Franklin Roosevelt was the best president since World War II. TwoTwo U.S. Two adults are selected at random from this sample without replacement. Complete parts (a) through (d).
(a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II.
(b) Find the probability that neither adult says Franklin Roosevelt was the best president since World War II.
(c) Find the probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II.
2. The probability that a person in the United States has type B+ blood is 12%. 4 unrelated people in the United States are selected at random. Complete parts (a) through (d).
(a) Find the probability that all five have type B+ blood.
(b) Find the probability that none of the five have type B+ blood.
(c) Find the probability that at least one of the five has type B+ blood.
3. A study found that 39% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty-five percent of the ART pregnancies resulted in multiple births.
(a) Find the probability that a random selected ART cycle resulted in a pregnancy and produced a multiple birth.
(b) Find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth.
(c) Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth? Explain.
In: Statistics and Probability
6.5 - 9 and 10)Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 84 and estimated standard deviation σ = 42. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.
(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)
__________________
(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.
The probability distribution of x is approximately normal with μx = 84 and σx = 42.
The probability distribution of x is approximately normal with μx = 84 and σx = 21.00.
The probability distribution of x is not normal.
The probability distribution of x is approximately normal with μx = 84 and σx = 29.70.
What is the probability that x < 40? (Round your answer to four decimal places.)___________
(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)___________
(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)____________
Question 10 ) Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6800 and estimated standard deviation σ = 2850. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.
(a) What is the probability that, on a single test, x
is less than 3500? (Round your answer to four decimal
places.)
_____________________
(b) Suppose a doctor uses the average x for two tests
taken about a week apart. What can we say about the probability
distribution of x?
The probability distribution of x is approximately normal with μx = 6800 and σx = 2850.The probability distribution of x is approximately normal with μx = 6800 and σx = 2015.25. The probability distribution of x is approximately normal with μx = 6800 and σx = 1425.00.The probability distribution of x is not normal.
What is the probability of x < 3500? (Round your answer
to four decimal places.)________
(c) Repeat part (b) for n = 3 tests taken a week apart.
(Round your answer to four decimal places.)_____________
In: Statistics and Probability
5 coins are put in a bag. 2 of the coins are weighted with the probability of flipping heads being three times as great than the probability of flipping tails; the remaining coins are fair. One of these coins is selected at random and then flipped once. What is the probability that a weighted coin was selected given that heads was flipped?
In: Statistics and Probability
Joe can choose to take the freeway or not for going to work.
There is a 0.4 chance for him to take the freeway. If he chooses freeway, Joe is late to work with probability 0.3; if he avoids the freeway, he is late
with probability 0.1
Given that Joe was early, what is the probability that he took freeway?
In: Math
A customer for a $50,000 fire insurance policy has a home in an area that may sustain a total loss in a given year with a probability of 0.001 and a 50% loss with a probability of 0.01. There is a 0.989 chance that the customer will make no claim in the coverage year. This same customer also wants a $20,000 renter’s insurance policy. The probability of a total loss is 0.005, the probability of a 50% loss is 0.015, and the probability of no loss is 0.98.
Let X be the company's loss on the fire policy and Y be the company's loss on the renter's policy.
Suppose the customer wants to increase the payout of the fire policy by 10% and the renter's insurance policy by 20%.
Find the variance of the combined policy, P = V(1.1X + 1.2Y), assuming the policy payouts are independent.
In: Statistics and Probability