Use the following population data for the next question(s). At a bird watching center, the number of yellow throated warblers observed over Memorial Day Weekend was: three on Saturday, 10 on Sunday, and eight on Monday. Assume sample sizes of two are randomly selected with replacement from this population.

10) List the nine different possible samples of yellow throated warblers and find the mean of each of them.

11) Identify the probability of each sample of yellow throated warblers and describe the sampling distribution of sample means.

12) Find the mean of the sampling distribution of yellow throated warblers.

13) Compare the mean of the sampling distribution of yellow throated warblers to the mean of the population of yellow throated warblers.

The table below shows the number of survey subjects who have received and not received a
speeding ticket in the last year, and the color of their car.

Speeding
ticket

No speeding
ticket

Tota
l
Red car 15 135 150
Not a red
car

45 470 515
Total 60 605 665

Find the probability that a randomly chosen person
a) Has a red car AND got a speeding ticket
b) Has a red car OR got a speeding ticket.
c) Does not have a red car OR did not get a speeding ticket.
d) did not get a speeding ticket, given that they drove a red car.
e) had a red car, given that they got a speeding ticket.

2.  The private marginal benefits for the flu vaccine is estimated to be MBp= 200-Q  where Q is the number of flu vaccines. The private marginal cost of producing the flu vaccine is MCp= 20. Because flu vaccines also reduce the probability that someone nearby receives the flu, there is a positive external benefit of MBe=100. No other externalities exist in the market.  

a. Solve for the market equilibrium price and quantity for flu vaccines. Solve the socially optimal level of price and quantity of flu vaccines (hint: MBS is the sum of MBP and MBE ).  

b. Graph all the curves and identify the deadweight loss area. Given the deadweight loss area you have identified in the graph, calculate the deadweight loss in the market.

Many manufacturers have quality control programs that include inspection of incoming materials for defects. Suppose that a computer manufacturer receives computer boards in lots of five. Two boards are randomly selected without replacement from each lot for inspection. We can represent possible outcomes of the selection process by pairs. For example, the pair (1,2) represents the selection of boards 1 and 2 for inspection regardless of the order of selection. Define r.v. X to be the number of defective boards observed among the two inspected.

(a) . By listing the ten different possible outcomes, find the probability distribution of X assuming that boards 1 and 2 are the only defective boards in a lot of five.

(b) . Calculate µX and σX.

In a Nuclear reactor a neutron of high speed (typically 10^7 m/s) must be slowed to 10^3 m/s so that it can have a high probability of interacting with isotope of Uranium (Atomic Number:92 , atomic mass:235) and causing it to fission. Show that a neutron can lose most of it's kinetic energy in an elastic collision with a light nuclei like deuterium or carbon which has a mass of only a few times the neutron mass. the material making up the light nuclei, usually heavy water (D2O) or graphite is called a moderator

Note ( Deuterium has mass 2m and carbon has mass 12m where m= mass of neutron)

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2932 and standard deviation 585. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that the customer consumes less than 2644 calories.

c. What proportion of the customers consume over 3200 calories?

d. The Piggy award will given out to the 2% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award?  calories. (Round to the nearest calorie)

A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a particular interest rate are normally distributed with a mean of 6 percent and a standard deviation of 1.7 percent. A single analyst is randomly selected. Find the probability that his/her forecast is

(a) At least 3.9 percent. (Round the z value to 2 decimal places. Round your answer to 4 decimal places.)

(b) At most 7 percent. (Round the z value to 2 decimal places. Round your answer to 4 decimal places.)

(c) Between 3.9 percent and 7 percent. (Round the z value to 2 decimal places. Round your answer to 4 decimal places.)

Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the

α=0.01

level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.

State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms.

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2833 and standard deviation 663. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that the customer consumes less than 2436 calories.  

c. What proportion of the customers consume over 3123 calories?  

d. The Piggy award will given out to the 2% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award?  calories. (Round to the nearest calorie)

Trevor is interested in purchasing the local hardware/electronic goods store in a small town in South Ohio. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 60% of the business days it is open. Estimate the probability that the store will gross over $850

1. at least 6 out of 10 business days.

0.68256

2. at most 3 of the 10 business days.

3. fewer than 7 out of 20 business days.

4. more than 16 out of 20 business days.

5. What is the expected (mean) number of business days for which the store would gross over $850 in a month (30 days)?