In one city, the probability that a person will pass his or her driving test on the first attempt is 0.68. Eleven people are selected at random from among those taking their driving test for the first time.

1. What is the probability that among these 11 people, exactly 7 people will pass their driving test for the first time?

a. 0.0144
b. 0.7437
c. 0.2326
d. 0.4890

2. What is the probability that among these 11 people, at least 7 people will pass their driving test for the first time?

a. 0.0144
  b. 0.7437
  c. 0.2326
  d. 0.4890

3. What is the probability that among these 11 people, at most 7 people will pass their driving test for the first time?

a. 0.5510
  b. 0.7437
  c. 0.2326
  d. 0.4890

4. What is the probability that among these 11 people, more than 7 people will pass their driving test for the first time?

a. 0.5110
  b. 0.7437
  c. 0.0308
  d. 0.4890

5. What is the probability that among these 11 people, the number passing the test is between 2 and 4 inclusive?

a. 0.5510
b. 0.7437
c. 0.0308
  d. 0.4890

Audrey and Diana go fishing at the Lyndon Fishing Pond. Upon arrival the owner informs them that the pond is stocked with an infinite number of independent fish, and that a typical fisher catches fish at a Poisson rate of 2 fish per hour. There are 8 other people fishing there that day. Diana has the same skill level as a typical fisher but Audrey catches on average twice as many fish as a typical fisher.

For the rest of the question, assume that 100 fish were caught that day.

Use those rounded probabilities in parts b), c) and d):
i. The probability a fish was caught by Audrey is 0.182
ii. The probability a fish was caught by Diana is 0.091
iii. The probability a fish was caught by someone else is 0.727

(c) (2) Find the probability that Audrey catches 15 fish and Diana catches 15 fish

(d) (2) Find the probability that Audrey and Diana catch 30 fish together

(e) (2) Given that Audrey catches 15 fish, find the probability that Diana catches 15 fish

(f) (2) Explain logically the difference between the probabilities in (c), (d), and (e)

The financial manager should attempt to maximize the wealth of the firm’s shareholders through achieving the highest possible value for the firm. a) Please explain how this concept is different from the idea of earning the highest possible profit for the firm

b) explain how social responsibility and ethical behavior on the part of corporate management affects the value of the firm;

Consider the following seven types of electromagentic waves: visible light, microwaves, radio waves, gamma rays, infrared, uv and x-rays

a) place the waves in order from shortest wavelength to longest

b)place the waves in order fromm lowest frequency to highest

c) which waves travels with the highest velocity in a vacuum

Burlington Mills produces denim cloth that it sells to jeans manufacturers. It is negotiating a new contract to provide cloth on a weekly basis to BJ Jeans. The demand for cloth from BJ Jeans is expected to vary each week according the following discrete probability distribution:

Demand (yd)
0 0.05

100 0.15 200 0.40 300 0.30 400 0.10

Burlington’s plant capacity available for this new job will vary each week because of other commitments and occasional breakdowns. Burlington estimates that available capacity will vary from 100 to 500 yards and follow a Uniform probability distribution (see note below).

Simulate the performance of the Burlington plant for 20 weeks. You may manually write your results provided your work is clear, neat, and easy to read. Attach your simulation to the Managerial Report.

Using your simulation results, determine the following:

1. Average weekly demand for cloth from BJ Jeans.

2. Average weekly available capacity for this contract at the Burlington plant.

3. Number of weeks that demand exceeds available plant capacity. Based on this result, also

   calculate the probability that demand will exceed available capacity.

Probability

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NOTE:

A Uniform probability distribution is one for which any value in a number interval is equally likely. In the Burlington example, then, available capacity will vary from 100 to 500 yards, with any value in this interval as probable as any other.

Since the calculator’s rand function returns a random real number from a Uniform distribution between 0.0 and 1.0, we can use it to model any Uniform distribution:

Low Value + rand*(High Value – Low Value)

For example, the weekly available capacity for the BJ Jeans contract varies uniformly from 100 to 500 yards. If in the simulation of some week, the rand function generates a value of 0.3486, then for that week the randomly selected available capacity will be:

100 + 0.3486*(500 – 100) = 239.44 yards

Question

The call center of a major energy provider expects to be particularly busy during the early shift in the early Winter. During the early shift calls arrive at a mean rate of 240 per hour and are believed to arrive at random.

(a) Explain briefly why it might be reasonable to expect these calls to arrive at random.

(b) What would be the probability distribution of the number of calls arriving during a five-minute period in the early shift? (There is no need to calculate any probabilities in this part of the question).

(c) Show (using probability tables or probability formulae) that the probability that there are more than 26 calls in a five-minute period is 0.0778. Show your working.

(d) Staffing levels during the early shift are such that they can cope with occasional peaks in arrivals, but service levels deteriorate rapidly when they experience a number of peaks close together. Continuing to assume that calls arrive at random, show that the probability that there are 6 or more five-minute periods in an hour in which the number of calls exceeds 26 is less than 1 in 1000. Show your working.

(e) Quiet periods only occur very rarely during the early shift in the call centre, so when gaps between calls exceed 2 minutes the management takes it as a signal of a telephone system failure and resets the system. What is the chance they reset the system unnecessarily in response to a 2 minute gap? Justify your method.

(f) You have seen in class how a Normal distribution can be used to approximate a Binomial distribution under certain conditions on n and p. (Remember that the Normal distribution was chosen to match the Binomial distribution in mean and standard deviation). A Normal distribution can also be used to approximate a Poisson distribution under certain conditions. By applying the same idea, use the Normal distribution to provide an approximate answer to part (c) above. Explain your method carefully.

(g) Suggest the conditions under which a Normal distribution can be used to approximate a Poisson distribution. Justify your answer.

There is a fair coin and a biased coin that flips heads with probability 1/4.You randomly pick one of the coins and flip it until you get a heads. Let X be the number of flips you need. Compute E[X] and Var[X]

In a lottery 4 numbers are picked from among 15 possible numbers. The player also purchases a lottery ticket and picks which four which he and she thinks will win.

a. construct the probability distribution of x, the number of winners picked by the player.

If we create a 5 digit bit string that is randomly generated, all strings equally likely...

1. possibility of string containing three consecutive zeroes?

2. conditional probability of it containing three consecutive zeroes where first number is a one?

FortyForty percent of consumers prefer to purchase electronics online. You randomly select 88 consumers. Find the probability that the number of consumers who prefer to purchase electronics online is​ (a) exactly​ five, (b) more than​ five, and​ (c) at most five.