Suppose the number of earthquakes occurring in an area approximately follows a Poisson distribution with an average rate of 2 earthquakes every year.

a.) Find the probability that there will be 1 to 3 (inclusive) earthquakes during the next year in this area.

b.) Find the probability that there will be exactly 5 earthquakes during the next 3 year period.

c.) Consider 10 randomly selected years during last century. What is the probability that there will be at least 3 of those years with no earthquake?

1) Imagine you roll a fair 4 sided dice 4 times.
what is the number of possible outcomes as a sum of successes?

2) What is the probability you will roll 3 successes, if the result of a 4 is considered a success?

3) what is the probability you will roll 3 or 4 successes, of the results of a 4 is considered a success?

4) what is the probability you will roll 3 or 4 successes. of the result of 3 or 4 is considered a success?

Although studies continue to show smoking leads to significant health problems, 20% of adults in the United States smoke. Consider a group of 280 adults.

If required, round your answers to four decimal places.

a. What is the expected number of adults who smoke?

b. What is the probability that fewer than 40 smoke?

c. What is the probability that from 35 to 70 (inclusive) smoke?

d. What is the probability that 70 or more smoke?

Since 1970, Super Rise, Inc., has provided maintenance services for elevators. On January 1, 2018, Super Rise obtains a contract to maintain an elevator in a 90-story building in New York City for 10 months and receives a fixed payment of $97,000. The contract specifies that Super Rise will receive an additional $48,500 at the end of the 10 months if there is no unexpected delay, stoppage, or accident during the year. Super Rise estimates variable consideration to be the most likely amount it will receive.

Required:
1. Assume that, because the building sees a constant flux of people throughout the day, Super Rise is allowed to access the elevators and related mechanical equipment only between 3am and 5am on any given day, which is insufficient to perform some of the more time-consuming repair work. As a result, Super Rise believes that unexpected delays are likely and that it will not earn the bonus. Prepare the journal entry Super Rise would record on January 1.
2. Assume instead that Super Rise knows at the inception of the contract that it will be given unlimited access to the elevators and related equipment each day, with the right to schedule repair sessions any time. When given these terms and conditions, Super Rise has never had any delays or accidents in the past. Prepare the journal entry Super Rise would record on January 31 to record one month of revenue.
3. Assume the same facts as requirement 1. In addition assume that, on May 31, Super Rise determines that it does not need to spend more than two hours on any given day to operate the elevator safely because the client’s elevator is relatively new. Therefore, Super Rise believes that unexpected delays are very unlikely. Prepare the journal entry Super Rise would record on May 31 to recognize May revenue and any necessary revision in its estimated bonus receivable.

Record any necessary entry on January 1.

Record any necessary entry on January 31 to record one month of revenue.

Record any necessary entry on May 31 to recognize May revenue and any necessary revision in its estimated bonus receivable.

QUESTION 4

You are considering investing either of the three stocks- A, B and C. The following table provides the information regarding the stocks

Based on the above information

1. Calculate the expected rate of returns and variance for each of the three stocks?

2. Calculate the coefficient of variation for each security?                                   

c) Your friend suggests you to purchase Stock A because the stock provides the highest return as compared to other stocks. If you are a risk averse investor, which stock should you choose? Justify your answer.                                                                                          (1 mark)                                                                                                                       

In the 1996 General Social Survey, for males age 30 and over, the following was true about respondents: • 11% of those in the lowest income quantile were college graduates. • 19% of those in the second income quantile were college graduates. • 31% of those in the third income quantile were college graduates. • 53% of those in the highest income quantile were college graduates. Find P(Q1|G), the probability that a randomly selected college graduate falls in the lowest income quartile. Also find P(Q2|G), P(Q3|G), and P(Q4|G). Discuss how this distribution compares to the unconditional distribution P(Q1), P(Q2), P(Q3), P(Q4)

What is probability that randomly selected 3-digit number (from 100 through 999) contains at least one of the digits 2 or 5?