Explain how to calculate the NPV (net present value) of an alternative.

What is the decision rule for adopting a project?

Suppose that the average waiting time for a patient at a physician's office is just over 29 minutes. In order to address the issue of long patient wait times, some physicians' offices are using wait-tracking systems to notify patients of expected wait times. Patients can adjust their arrival times based on this information and spend less time in waiting rooms. The following data show wait times (minutes) for a sample of patients at offices that do not have a wait-tracking system and wait times for a sample of patients at offices with a wait-tracking system.

Give a brief discussion, comparing and contrasting unit theory learning curves and cumulative average theory learning curves.  Include a discussion of what the impact might be if you incorrectly used a unit theory curve in lieu of a cumulative average theory curve, and vice versa.

Brothers and sisters: Thirty students in a first-grade class were asked how many siblings they have. Following are the results.

2. A lawyer believes that a certain judge imposes prison sentences for property crimes that are longer than the state average 11.7 months. He randomly selects 36 of the judge’s sentences and obtains mean 13.8 and standard deviation 3.9 months.

a) Test the hypothesis at 1% significance level.

b) Construct a 99% confidence interval for the true average length of sentences im- posed by this judge.

c) Construct a 95% confidence interval for the true average length of sentences im- posed by this judge.

d) Compare the margins of error from b) and c).

The payoff X of a lottery ticket in the Tri-State Pick 3 game is $500 with probability 1/1000 and $0 the rest of the time. Assume the payoffs X and Y are for separate days and are independent from each other.

a. What price should Tri-State charge for a lottery ticket so that they can break even in the long run (average profit =$ 0).

b. Find the mean and standard deviation of the total payoff X+Y.

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 41 farming regions gave a sample mean of x bar = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.92 per 100 pounds. (a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop (in dollars). What is the margin of error (in dollars)? (For each answer, enter a number. Round your answers to two decimal places.) lower limit $ upper limit $ margin of error $ (b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.39 for the mean price per 100 pounds of watermelon. (Enter a number. Round up to the nearest whole number.) farming regions (c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop (in dollars). What is the margin of error (in dollars)? Hint: 1 ton is 2000 pounds. (For each answer, enter a number. Round your answers to two decimal places.) lower limit $ upper limit $ margin of error $

An insurance company has three types of annuity products: indexed annuity, fixed annuity, and variable annuity. You are given:

• None of the customers have both fixed annuity and variable annuity.
• 40% of the customers with fixed annuity also have indexed annuity.
• Half of the customers with two annuity products have variable annuity.
• 60% of the customers have indexed annuity.
• The number of customers who have only the variable annuity is the same as the number of customers who have two annuity products.
• All customers have at least one type of annuity.

Determine the proportion of the customers who only have the indexed annuity.

1. A coin is tossed 100 times, each resulting in a tail (T) or a head (H). If a coin results in a head, Roy have to pay Slim 500$. If the coin results in a tail, Slim have to pay Roy 500$. What is the probability that Slim comes out ahead more than $20,000?

Tell how you currently use statistics at a bank. Be descriptive in 250 words or more. Please typed answers only.

Part 1.

When a probability experiment only has two possible outcomes and you know the probability of one outcome, you can find the probability of the other outcome by computing (the complementary probability, using the addition rule, using the multiplication rule)

To find the probability of two (mutually exclusive, independent) events both occurring, you may simply multiply their individual probabilities.

When two scenarios are (mutually exclusive, independent) , we can simply add their probabilities together to find the probability that one scenario or the other scenario occurs.

Part 2.

When using the choose function, the top number n represents (number of successes, number of trials, probability) and the bottom number k represents (number of trials, probability, number of successes )

Part 3.

Suppose you flip a coin 6 times. For each of the 6 trials there are 2 possible outcomes, heads or tails. Heads and tails each have a probability of 0.5 per trial. Consider "heads" to be a success. What is the probability that you only have 2 successes in 6 trials? Round your answer to four digits after the decimal point.

The report "Progress for Children" (UNICEF, April 2005) included the accompanying data on the percentage of primary-school-age children who were enrolled in school for 19 countries in Northern Africa and for 23 countries in Central Africa.

We will construct a comparative stem-and-leaf display using the first digit of each observation as the stem and the remaining two digits as the leaf. To keep the display simple the leaves will be truncated to one digit. For example, the observation 54.6 would be processed as

54.6 → stem = 5, leaf = 4 (truncated from 4.6),

the observation 96.1 would be processed as

96.1 → stem = ? , leaf = ? (truncated from 6.1)

and the observation 35.5 would be processed as

35.5 → stem = ? , leaf = ?(truncated from 5.5).

The resulting comparative stem-and-leaf display is shown in the figure below.

Comparative stem-and-leaf display for percentage of children enrolled in primary school.

From the comparative stem-and-leaf display we can see that there is quite a bit of variability in the percentage enrolled in school for both Northern and Central African countries and that the shapes of the two data distributions are quite different. The percentage enrolled in school tends to be higher in Northern African countries than in Central African countries, although the smallest value in each of the two data sets is about the same. For Northern African countries the distribution of values has a single peak in the 90s with the number of observations declining as we move toward the stems corresponding to lower percentages enrolled in school. For Central African countries the distribution is more symmetric, with a typical value in the mid 60s.

How many individual stem-and-leaf displays are represented by the comparative stem-and-leaf display?

-one

-two     

-three

-It can't be represented as simple stem-and-leaf display.

Paul wants to estimate the mean number of siblings for each student in his school. He records the number of siblings for each of 100 randomly selected students in the school. What is the parameter? Select the correct answer below: all the students in the school the 100 randomly selected students the specific number of siblings for each randomly selected student the mean number of siblings for all students in the school the mean number of siblings for the randomly selected students

Part 1.

About 24% of flights departing from New York's John F. Kennedy International Airport were delayed in 2009. Assuming that the chance of a flight being delayed has stayed constant at 24%, we are interested in finding the probability of 10 out of the next 100 departing flights being delayed. Noting that if one flight is delayed, the next flight is more likely to be delayed, which of the following statements is correct?

• We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.
• We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another.
• We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.
• We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this probability.

Part 2.

A July 2011 Pew Research survey suggests that 27% of adults say they regularly get news through Facebook, Twitter or other social networking sites. What's the probability that in a random sample of 10 people at most 1 of them get their news through social networking sites?

A July 2011 Pew Research survey suggests that 27% of adults say they regularly get news through Facebook, Twitter or other social networking sites. What's the probability that in a random sample of 10 people at most 1 of them get their news through social networking sites?

• 0.20
• 0.96
• 0.16
• 0.04
• 0.06

Part 3.

3.32 Arachnophobia: A 2005 Gallup Poll found that 7% of teenagers (ages 13 to 17) suffer from arachnophobia and are extremely afraid of spiders. At a summer camp there are 10 teenagers sleeping in each tent. Assume that these 10 teenagers are independent of each other.


(a) Calculate the probability that at least one of them suffers from arachnophobia.
(please round to four decimal places)
(b) Calculate the probability that exactly 2 of them suffer from arachnophobia?
(please round to four decimal places)
(c) Calculate the probability that at most 1 of them suffers from arachnophobia?
(please round to four decimal places)

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 67 professional actors, it was found that 36 were extroverts.

(a)

Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b)

Find a 95% confidence interval for p. (Round your answers to two decimal places.)
lower limit          
upper limit          

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 5% confident that the true proportion of actors who are extroverts falls above this interval.We are 95% confident that the true proportion of actors who are extroverts falls within this interval.     We are 5% confident that the true proportion of actors who are extroverts falls within this interval.We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

(c)

Do you think the conditions n·p > 5 and n·q > 5 are satisfied in this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.     Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.