You are the auditor for a company and need to review the company’s accounts receivable using probability proportional to size (PPS) sampling. In addition, the board of directors has requested that you and your team present an explanation of your PPS process at its next monthly meeting.

-The recorded book value of these accounts is $3,460,000.

-The company has a tolerable error of $63,460.

-The anticipated error is $13,000.

-The risk of incorrect acceptance is 5%.

-The acceptable number of overstatements of misstatements is 2.

Use probability proportional to size (PPS) sampling to do the following:

a. Determine the reliability factor.

b. Determine the correct expansion factor.

c. Determine the sample size you should use.

d. Determine the sampling interval you should use.

A study randomly selected 100 samples, each of which consisted of 100 people, and recorded the number of left-handed people, X. The table below shows the probability distribution of the data. Find the mean and the standard deviation of the probability distribution using Excel.

• Round the mean and standard deviation to two decimal places.

Part 1 Select the appropriate discrete probability distribution. If using a binomial distribution, use the constant probability from the collected data and assume a fixed number of events of 20. If using a Poisson distribution, use the applicable mean from the collected data. art 2 Using the mean and standard deviation for the continuous data, identify the applicable values of X for the following: Identify the value of X of 20% of the data, identify the value of X for the top 10% of the data, and 95% of the data lies between two values of X.

Mean 4.84 Median 4

Standard Deviation 3.161645141 Sample Variance 9.996

Data

1.5

1.2

2.3

2.7

3.5

4.5

6

7.8

9.4

9.5

Suppose that the weights of airline passenger bags are normally distributed with a mean of 48.01 pounds and a standard deviation of 3.6 pounds.

a) What is the probability that the weight of a bag will be greater than the maximum allowable weight of 50 pounds? Give your answer to four decimal places.

b) Assume the weights of individual bags are independent. What is the expected number of bags out of a sample of 11 that weigh greater than 50 lbs? Give your answer to four decimal places.

c) Assuming the weights of individual bags are independent, what is the probability that 4 or fewer bags weigh greater than 50 pounds in a sample of size 11? Give your answer to four decimal places.

5. Nineteen people move out of a neighborhood; four are minorities. Of the nineteen, eight move onto a block with new housing, and one of these eight is a minority. How likely is it that, if there were no discrimination, less than two people out of the eight people on this new block would be minorities? If the resulting probability is less than 0.05, evidence for discrimination exists. Does such evidence exist in this case?

6. There is an average of four accidents per year at a particular intersection.   What is the probability of more than one accident there next month? Hint: Use 1 month = 1/12 of a year to first get the number of accidents that are expected next month.   

Please Help I cant figure this out !!!

Genetic theory predicts that, in the second generation of a cross of sweet pea plants, flowers will be either red or white, with each plant having a 25% chance of producing red flowers. Flower colours of separate plants are independent. Let X be the number of plants with red flowers out of 20 plants selected at random from the second generation of this cross. (a) What is the probability distribution of X? [3] (b) Calculate: (i) the mean and standard deviation of X. [3] (ii) P( X > 8) [2] (iii) P( 4 ≤ X ≤ 10) [2] (c) If only 3 of the 20 plants had red flowers, would this be an unusual sample? Calculate a probability and use it to justify your answer

The number of floods that occur in a certain region over a given year is a random variable having a Poisson distribution with mean 2, independently from one year to the other. Moreover, the time period (in days) during which the ground is flooded, at the time of an arbitrary flood, is an exponential random variable with mean 5. We assume that the durations of the floods are independent. Using the central limit theorem, calculate (approximately)
(a) the probability that over the course of the next 50 years, there will be at least 80 floods in this region. Assume that we do not need to apply half-unit correction for this question.

(b) the probability that the total time during which the ground will be flooded over the course of the next 50 floods will be smaller than 200 days.

The mean and standard deviation for the diameter of a certain type of steel rod are mu = 0.503 cm and sigma = 0.03cm. Let X denote the average of the diameters of a batch of 100 such steel rods. The batch passes inspection if Xbar falls between 0.495 and 0.505cm.

1. What is the approximate distribution of Xbar? Specify the mean and the variance and cite the appropriate theorem to justify your answer.

2. What is the approximate probability the batch will pass inspection?

3. Over the next six months 40 batches of 100 will be delivered. Let Y denote the number of batches that will pass inspection.

(a) the distribution of Y is: Binomial, hypergeometric, negative binomial, OR poisson?

(b) give the approximation, as accurately as possible, to the probability P(Y ≤ 30).

5.)

The average time to run the 5K fun run is 21 minutes and the standard deviation is 2.7 minutes. 45 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
4. If one randomly selected runner is timed, find the probability that this runner's time will be between 20.7962 and 21.3962 minutes.
5. For the 45 runners, find the probability that their average time is between 20.7962 and 21.3962 minutes.
6. Find the probability that the randomly selected 45 person team will have a total time more than 927.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. The top 10% of all 45 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes

6.)

Each sweat shop worker at a computer factory can put together 4.1 computers per hour on average with a standard deviation of 0.9 computers. 17 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
4. If one randomly selected worker is observed, find the probability that this worker will put together between 4.2 and 4.4 computers per hour.
5. For the 17 workers, find the probability that their average number of computers put together per hour is between 4.2 and 4.4.
6. Find the probability that a 17 person shift will put together between 66.3 and 68 computers per hour.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. A sticker that says "Great Dedication" will be given to the groups of 17 workers who have the top 20% productivity. What is the least total number of computers produced by a group that receives a sticker? minutes (round to the nearest computer)

HOUSE OF REPRESENTATIVES

SENATE

COMBINED TABLE – CONGRESS COMBINING HOUSE OF REPRESENTATIVES AND SENATE

Congress if made up of the House of Representatives and the Senate. Members of the House of Representatives serve two year terms and represent a district in a state. The number of representatives each state has is determined by population. States with larger populations have ore representatives than stats with smaller populations. The total number of representatives is set by law at 435 members. Members of the Senate serve sex-year terms and represent a state. Each state has 2 senators, for a total of 100. The tables show the makeup of the 111^th Congress by gender and political party. There are two vacant seats in the House of Representatives.

Please answer the questions below and SHOW YOUR WORK where applicable.. all answers should be proportions rounded to the nearest thousandths (3 decimals) for instance this is what is required to be shown if I ask and answer the following question:

Find the probability that a Senate is a Male or a Democrat:

83/100   +    57/100     –     44/100     =      96/100   =    .960

1. Find the probability that a randomly selected House of Representative is a female.

2. Find the probability that a randomly selected Senator is a female.

3. A House of Representative member is selected at random. Find the probability of each event:
   1. The representative is a male

2. The representative is a Republican

3. The representative is a male GIVEN that the representative is a Republican

4. The representative is female and a Democrat

4. A Senator is selected at random. Find the probability of each event
   1. The senator is a male

2. The senator is not a Democrat

3. The senator is female or a Republican

4. The senator is a male or a Democrat

5. Using the same row and column headings, create a combined table for the Congress (template created for you above)

6. A member of Congress is selected at random. Use the combined table to find the probability of each event.

1. The member is Independent

2. The member is female and a Republican

3. The member is male or a Democrat