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andriy [413]
3 years ago
7

Suppose Securitex is a small firm that has developed a new​ anti-theft device for automobiles. Securitex currently sells its dev

ice online and earns profit of ​$7 million per year. GM is considering installing​ Securitex's system on its automobiles. The two firms​ first, however, must bargain over what price GM will pay Securitex for its software
Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
4 0

Question:

Suppose Securitex is a small firm that has developed a new anti-theft device for automobiles. Securitex currently sells its device online and earns profit of $7 million per year. GM is considering installing Securitex's system on its automobiles. The two firms first however, must bargain over what price GM will pay Securitex for its software. GM chooses how much to offer Securitex for its system and then Securitex chooses whether to accept the offer and install its system on GM's automobiles. The strategies and corresponding profits for GM (GM) and Securitex (SX) are depicted in the decision tree to the right. Profits are in millions: and GM's payoffs represent the additional profit it can earn on its automobiles with Securitex's anti-theft system. What is the subgame-perfect equilibrium?

A. The subgame-perfect equilibrium is for GM to offer a high price and for Securitex to reject the offer.

B. The subgame-perfect equilibrium is for GM to offer a low price and for Securitex to accept the offer.

C. The subgame-perfect equilibrium is for GM to offer a high price and for Securitex to accept the offer.

D. The subgame-perfect equilibrium is for GM to offer a low price and for Securitex to reject the offer.

E. A subgame-perfect equilibrium does not exist for this game.

Answer:

The correct option is;

C. The​ subgame-perfect equilibrium is for GM to offer a highhigh price and for Securitex to accept the offer.

Explanation:

A subgame perfect equilibrium is a improvement of a Nash equilibrium implemented in dynamic games (i. e. the interactions between GE will take place time and over again and their decision at a point will have an effect on the present and upcoming returns

A subgame perfect is a strategy profile is that constitute a Nash equilibrium of all possible subgames of the actual game.

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Answer:

To calculate the relative frequency, first we need to know what exactly is and how to calculate it.

Relative frequency is the ratio between the absolute frequency (how many repetitions have a specific outcome) and the total outcomes. Also, this type of frequency is used to show the representation that some data have over the whole distribution.

So, in this case, we need to just divide 13, which belongs to red marble's results, to 60 which is the total outcomes, as it's presented:

         13redmarble                                                                                                                       Fr = -------------------------

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Normally, relative frequency is shown as a percentage multiplying this result by 100. Therefore, 22% is the approximate percentage of the relative frequency, which means that 22% is the representation of red marbles outcomes of the whole distribution, or we can say it as a probability: there's 22% of chances when someone extract a marble, it will be red.

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jenyasd209 [6]

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Step-by-step explanation:

Area is length × height

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Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with
Alexxandr [17]

Answer:

Step-by-step explanation:

Hello!

The SAT math scores have a normal distribution with mean μ= 540 and standard deviation σ= 119

Eleonor scored 680 on the math part.

X: score obtained in the SAT math test

*-*

The ACT Assessment math test has a normal distribution with mean μ= 18.2 and standard deviation σ= 3.6

Gerald took the test and scored 27.

X: score obtained in the ACT math test

a.

To standardize the values you have to use the following formula:

Z= (X-μ)/σ ~N(0;1)

For each score, you have to subtract its population mean and divide it by the standard deviation.

Eleonor score:

Z= (680-540)/119= 1.176 ≅ 1.18

Gerald Score

Z= (27-18.2)/3.6= 2.44

b.

Since both variables are very different you cannot compare the "raw" scores to know which one is higher but once both of them were standardized, you can make a valid comparison.

In this case, Eleonor's score is 1.18σ away from the mean, while Gerald's score is 2.44σ away, i.e. Gerald's score is further away from the mean score than Eleonor's so his score is higher.

c.

In this item, you are asked to find the value that divides the top 10% of the population from the bottom 90%.

Symbolically you can express it as:

P(Z>c)=0.1

or

P(Z≤c)= 0.9

The tables of standard normal distribution show accumulative probabilities of P(Z<Z₁₋α), sois best to use the second expression.

In the body of the distribution table, you have to look for a probability of 0.90 and then reach the corresponding Z value looking at the table margins. The first column shows the integer and first decimal digit, the first row shows the second decimal digit. So the corresponding value of Z is 1.28

Now you have to reverse the standardization to know the corresponding scores for each test.

SAT test score:

Z= (c-μ)/σ

Z*σ = c-μ

c = (Z*σ ) + μ

c= (1.28*119)+540

c= 692.32

The student should score 692.32 in his SAT math test to be in the top 10% of the population.

ACT test score

Z= (c-μ)/σ

Z*σ = c-μ

c = (Z*σ ) + μ

c= (1.28*3.6)+18.2

c= 22.808 ≅ 22.81

The student should score 22.81 in his ACT math test to be in the top 10% of the population.

d.

In this item, their vas a sample of students that took the ACT taken and you need to calculate the probability of the sample mean being greater than 25.

If you were to take a 100 random samples of ACT scores of 100 students and calculate the mean of all of them, you will get that the sample mean is a random variable with the same kind of distribution as the original variable but it's variance will be influenced by the sample size. In this case, the original variable is:

X: score obtained in the ACT math test

This variable has a normal distribution X~N(μ;δ²), then it's the sample mean will also have a normal distribution with the following parameters X[bar]~N(μ;δ²/n)

Remember when you standardize a value of the variable of interest you subtract its "mean" and divide it by its "standard deviation" in this case the mean is μ and the standard deviation will be √(δ²/n) ⇒ δ/√n and the formula of the standard normal is:

Z= (X[bar]-μ)/(δ/√n)~N(0;1)

with n=100

μ= 18.2

δ= 3.6

P(X[bar]>25)= 1 - P(X[bar]≤25)

1 - P(Z≤(25-18.2)/(6.3/√100))= 1 - P(Z≤10.79)= 1 - 1 = 0

The probability of the mean ACT score for a random sample of 100 students being more than 25 is zero.

I hope it helps!

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3 years ago
The repairs to Ryan's bike cost more than $50. Write an inequality that represents the cost of repairs r.
Talja [164]

If r is the cost of repairs, then the inequality is:

r > 50

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