identify the type of distribution AND the probability asked for
a. a shockproof ballpen is subjected to a shock test wherein a ballpen is dropped on a floor a certain number of times. the probability that the ballpen will stop working is 0.22. let X be the number of falls in order for a ballpen to stop writing. find the probability that the pen is dropped 12 times in order for it to stop writing.

b. ilaw company delivers candles to its customers in boxes of 20. it has been discovered that 6 candles in every box won't light properly. a customer randomly selects 5 candles from a box, and demands to return the candles if at least 4 of the candles he picked will not light properly. let x denote the number of candles that won't light. what is the probability that the customer will return the candles ordered?

c. in a coffee shop, 45% of the customers prefer frapuccino. what is the probability that 6 of the bext 10 customers who will walk into the coffee shop will order frapuccino? let x be the number of customers who will choose a frapuccino drink?

identify the type of distribution AND the probability asked for
a. a shockproof ballpen is subjected to a shock test wherein a ballpen is dropped on a floor a certain number of times. the probability that the ballpen will stop working is 0.22. let X be the number of falls in order for a ballpen to stop writing. find the probability that the pen is dropped 12 times in order for it to stop writing.

b. ilaw company delivers candles to its customers in boxes of 20. it has been discovered that 6 candles in every box won't light properly. a customer randomly selects 5 candles from a box, and demands to return the candles if at least 4 of the candles he picked will not light properly. let x denote the number of candles that won't light. what is the probability that the customer will return the candles ordered?

c. in a coffee shop, 45% of the customers prefer frapuccino. what is the probability that 6 of the bext 10 customers who will walk into the coffee shop will order frapuccino? let x be the number of customers who will choose a frapuccino drink?

According to an? airline, flights on a certain route are on time 80?% of the time. Suppose 13 flights are randomly selected and the number of? on-time flights is recorded. ?(a) Explain why this is a binomial experiment. ?(b) Find and interpret the probability that exactly 8 flights are on time. ?(c) Find and interpret the probability that fewer than 8 flights are on time. ?(d) Find and interpret the probability that at least 8 flights are on time. ?(e) Find and interpret the probability that between 6 and 8 ?flights, inclusive, are on time. ?(a) Identify the statements that explain why this is a binomial experiment. Select all that apply. A. There are two mutually exclusive? outcomes, success or failure. B. The trials are independent. C. The probability of success is the same for each trial of the experiment. D. There are three mutually exclusive possibly? outcomes, arriving? on-time, arriving? early, and arriving late. E. The experiment is performed a fixed number of times. F. Each trial depends on the previous trial. G. The experiment is performed until a desired number of successes is reached. ?(b) The probability that exactly 8 flights are on time is nothing. ?(Round to four decimal places as? needed.) Interpret the probability. In 100 trials of this? experiment, it is expected about nothing to result in exactly 8 flights being on time. ?(Round to the nearest whole number as? needed.) ?(c) The probability that fewer than 8 flights are on time is nothing. ?(Round to four decimal places as? needed.)

The Super Bowl Indicator Theory suggests that the stock market will have a positive year if the team in the National Football Conference, or a team with an NFC origin, wins. If the American Football Conference team wins, the market will fall. According to the recent news (MarketWatch, 2/6/2017), it has accurately predicted the direction of the market for the year following 40 of the 50 Super Bowls since the first super bowl in 1967. Why do we have such phenomena? Is the finding consistent with market efficiency? Please explain...I may have further questions..

1. If A and B are mutually exclusive events, does it follow that An and B cannot be independent events ? Give an example to demonstrate your answer. For example, discuss an election where only one person can win. Let A be the event that party A’s candidate wins, let B be the event that party B’s candidate wins. Does the outcome of one event determine the outcome of the other event ? Are A and B mutually exclusive events ?

2.Conditions under which P(A and B) = P(A) * P(B) is true. Under what conditions is this not true ?

1. Company A is currently suing company B for IP infringement. Their stock prices currently are pA = $10 and pB = $8. If A wins the lawsuit, its stock will go up to $15 and B’s stock will drop to $5. If A loses, however, its stock will be worth $9, and B’s stock will rise to $10. Neither stock pays dividends. Assume no arbitrage and consider whether A wins or not to represent the only two states of the world.

a. Calculate the Arrow-Debreu security prices, qA-wins and qA-loses.

b. If there is a riskless asset in the economy that pays $1 in both states, what would the price of such asset be? What would be the riskless interest rate?

c. Now suppose there actually is a “riskless bond” in the economy that offers a 5% interest rate between now and when the outcome of the lawsuit is announced. Is there an arbitrage opportunity? If so, how might you trade to exploit it? (Note the asset we priced in part b is not assumed to exist, nor are Arrow Debreu securities.)

A biologist estimates that the chance of germination for a type of bean seed is 0.8. A student was given 10 seeds. Let Xbe the number of seeds germinated from 10 seeds.

a) Assuming that the germination of seeds is independent, explain why the distribution of Xis binomial.

b) What are the values of nand p?

c) What is the mean and standard deviation of the number of seeds that germinate?

d) What is the probability that all seeds germinate?

e) What is the probability that only one seed does not germinate?

f) What is the probability that at most four seeds germinate?

g) Suppose that a group of students plant 200 seeds. What is the mean and standard deviation of the number that germinate?

h) What is the probability that at least 150 of the seeds germinate?

Chapter 3 Section 7 Problem 2

We have 22 female and 26 male patients in the hospital. I am going to select 36 of these patients for transfer to another hospital.

(a) What is the expected number of female patients to be transferred

(b) What is the probability that the same number of male and female patients transferred?

Chapter 3 Section 8 Problem 2

The number of flowers on my balcony follows a Poisson distribution with a mean of 0.25 per square foot.

a) What is the probability of two or more flowers per square foot?

b) What is the probability of no flowers in 5 square feet?

c) What is the probability of two or fewer flowers in 5 square feet?

Mimi plans to make a random guess at 5 true-or-false questions.

a. Assume random number X is the number of correct answers Mimi gets. As we know, X follows a binomial distribution. What is n (the number of trials), p (probability of success in each trial) and q (probability of failure in each trial)?

b. How many correct answers can she expect to get?

Mimi plans to make a random guess at a test containing 5 true-or-false questions.

a. Mimi plans to make a random guess at 5 true-or-false questions. What is the probability that Mimi will pass the test by random guess?

b. What function can be used to find the probability?

In a certain area of New York State with a large population, 70% of drivers use chains on the car tires for winter driving. A random sample of 16 drivers is taken. You are interested in the number of drivers in the sample that use chains while driving.

a. Find the probability that at least 11 drivers in the sample use chains.

b. Find the probability that at most 11 drivers in the sample use chains.

c. Find the probability that less than 11 drivers in the sample use chains.

d. Find the mean and standard deviation of the number of drivers in the sample that use chains.

e. Find the probability that the number of drivers in the sample that use chains is within 1 standard deviation of its mean.