A consumer response team hears directly from consumers about the challenges they face in the​ marketplace, brings their concerns to the attention of financial​ institutions, and assists in addressing their complaints. The consumer response team accepts complaints related to​ mortgages, bank accounts and​ services, private student​ loans, other consumer​ loans, and credit reporting. An analysis of complaints over time indicates that the mean number of credit reporting complaints registered by consumers is 1.55 per day. Assume that the number of credit reporting complaints registered by consumers is distributed as a Poisson random variable. Complete parts​ (a) through​ (d) below. a. What is the probability that on a given​ day, no credit reporting complaints will be registered by​ consumers? The probability that no complaints will be registered is nothing. ​(Round to four decimal places as​ needed.) b. What is the probability that on a given​ day, exactly one credit reporting complaint will be registered by​ consumers? The probability that exactly one complaint will be registered is nothing. ​(Round to four decimal places as​ needed.) c. What is the probability that on a given​ day, more than one credit reporting complaint will be registered by​ consumers? The probability that more than one complaint will be registered is nothing. ​(Round to four decimal places as​ needed.) d. What is the probability that on a given​ day, fewer than two credit reporting complaints will be registered by​ consumers? The probability that fewer than two complaints will be registered is nothing. ​(Round to four decimal places as​ needed.)

Skyline pizza is a famous restaurant operating a number of outlets. The restaurant uses a toll-free telephone number to book pizzas at any of its outlets. If the clerk is occupied on one line, incoming phone calls to the restaurant are answered automatically by an answering machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls come in at a rate of about 15 per hour. The clerk is capable of taking an order in an average of 3 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The clerk is paid $20 per hour, but because of lost goodwill and sales, CWD loses about $50 per hour of customer time spent waiting for the clerk to take an order.

Part A Answer the following questions:

a. What is the probability that no customers are in the system (Po)? 2 marks

b. What is the average number of customers waiting for service ( Lq)? 3 marks

c. What is the average number of customers in the system (L)?-2 marks

d. What is the average time a customer waits for service(Wq)? 3 marks

e. What is the average time in the system (W) ?-3 marks

f. What is the probability that a customer will have to wait for service (Pw)?-2 marks

g What is the probability that there is exactly 2 customers in the system- 2 marks

h) What is the probability that there are more than 3 customers in the system-3 mark

Part B

Skyline is considering adding a second clerk to take calls. The store would pay that person the same $20 per hour.

Using appropriate formula for the multiple channel model, answer the following questions:

a. What is the probability that no customers are in the system (Po)? 3 marks

b. What is the average number of customers waiting for service (Lq)? 2 marks

c. What is the average number of customers in the system (L)? 3 mark

s d. What is the average time a customer waits for service (Wq)? 2 marks

e. What is the average time in the system (W)? 2 marks

f. What is the probability that a customer will have to wait for service (Pw)? 2 marks

g. What is the probability that there is exactly 2 customers in the system 2 marks

h. Should it hire another clerk? Explain by showing the cost savings - 4 marks

1) Scores for a common standardized college aptitude test are normally distributed with a mean of 495 and a standard deviation of 108. Randomly selected men are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the preparation course has no effect.

If 1 of the men is randomly selected, find the probability that his score is at least 551.9.
P(X > 551.9) =  
Enter your answer as a number accurate to 4 decimal places.

If 13 of the men are randomly selected, find the probability that their mean score is at least 551.9.
P(M > 551.9) =  
Enter your answer as a number accurate to 4 decimal places.

Assume that any probability less than 5% is sufficient evidence to conclude that the preparation course does help men do better. If the random sample of 13 men does result in a mean score of 551.9, is there strong evidence to support the claim that the course is actually effective?

• Yes. The probability indicates that it is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 551.9.
• No. The probability indicates that it is too possible by chance alone to randomly select a group of students with a mean as high as 551.9.

2) Scores for a common standardized college aptitude test are normally distributed with a mean of 495 and a standard deviation of 115. Randomly selected men are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the preparation course has no effect.

If 1 of the men is randomly selected, find the probability that his score is at least 528.4.
P(X > 528.4) =  
Enter your answer as a number accurate to 4 decimal places.

If 20 of the men are randomly selected, find the probability that their mean score is at least 528.4.
P(M > 528.4) =  
Enter your answer as a number accurate to 4 decimal places.

Assume that any probability less than 5% is sufficient evidence to conclude that the preparation course does help men do better. If the random sample of 20 men does result in a mean score of 528.4, is there strong evidence to support the claim that the course is actually effective?

• No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 528.4.
• Yes. The probability indicates that is is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 528.4.

Scrapper Elevator Company has 20 sales representatives who sell its product throughout the United States and Canada. The number of units sold last month by each representative is listed below. Assume these sales figures to be the population values. 2 3 2 3 3 4 2 4 3 2 2 7 3 4 5 3 3 3 3 5 picture Click here for the Excel Data File Draw a graph showing the population distribution. (Click on the x-axis exactly below the "0" point and then drag the bar till it reaches the correct answer.) Compute the population mean. (Round your answer to 1 decimal place.) Compute the standard deviation. (Round your answer to 2 decimal places.) If you were able to list all possible samples of size five from this population of 20, how would the sample means be distributed? What would be the mean of the sample means? (Round your answer to 2 decimal places.) What would be the standard deviation of the sample means? (Round your answer to 2 decimal places.)?

1/ determine where the following statement is true the probability that event a will occur is P(A)= number of succesful outcomes/ number of unsuccessful outcomes

true or false

2/ one hundred people were asked " do you favor stronger laws on gun control?" Of the 33 that answered "yes" to the question, 14 were male . Of the 67 that answered "no" to the question , six were male . If one person is selected at random, what is the probability that this person answered "yes" or was a male? Round to nearest hundredth.

0.53 or 0.67 or 0.13 or 0.39

3/ numbered disks are placed in a box and one box is selected at random. There are 6 red disks numbered 1 through 6 and 7 yellow disks numbered 7 through 13. In an experiment a disk is selected , the number and color noted replaced, and then a second disk is selected is this an example of independence? Yes or no

4/ a single 6 sided die is rolled twice. Find the probability of getting a 2 the first time and 1 the second time. Express the probability as a simplified fraction

A: 1/36. B: 1/12. C : 1/6. D: 1/3

Three patients have made appointments to have their blood pressure checked at a clinic. As each patient is selected, he/she is tested. If he/she has high blood pressure, a success (S) occurs; if he/she does not have high blood pressure, a failure (F) occurs. Let x be the number of persons who have high blood pressure (i.e., Let x represent the number of successes among the three sampled persons).

a. How many outcomes should you have from this probability experiment?

b. Construct a tree diagram for the number of persons who have high blood pressure.

c. List all outcomes from this probability experiment.

d. What are the possible values for x?

e. Construct the probability distribution of x.

f. Determine whether the table represents a discrete probability distribution. Explain

g. Find P(x=1)=

h. Find P( x ≤ 2)=

i. Find P(x >2)=

j. Find P (x ≥ 2)=

k. Find (x=0)=

l. Compute the mean,

m. Compute the variance,

n. Compute the standard deviation,

The number of wooden sailboats constructed per month in a small shipyard is a random variable that obeys the probability distribution given in Table below: Probability distribution of monthly Number of Sailboats /Probability( 2 is the sailboat and 0.15 is probability; likewise please consider in this way for the rest of the data) 2, 0.15; 3, 0.20; 4, 0.30; 5, 0.25; 6, 0.05; 7,0.05; Suppose that the sailboat builders have fixed monthly costs of $30,000 and an additional construction cost of $4,800 per boat. (a) Compute the mean and standard deviation of the number of boats constructed each month. (b) What is the mean and standard deviation of the monthly cost of the sailboat construction operation? 4 (c) How do your answers in part (b) change if the fixed monthly cost increases from $30,000 to $53,000? Try to compute your answer using the results of the calculation in part (b) only. (d) How do your answers in part (b) change if the construction cost per boat increases from $4,800 to $7,000, but the fixed monthly cost stays at $30,000? Try to compute your answer using the results of the calculations of parts (a) and (b) only.

Meiosisis the process in which a diploid cell that contains two copies of the genetic material produces an haploid cell with only one copy (sperms and eggs). The resulting molecule of genetic material is linear molecule that is composed of consecutive segments: a segment that originated from one of the two copies followed by a segment from the other copy and vice versa. The border points between segments are called points of crossover. The Haldane model for crossovers states that the number of crossovers between two loci on the genome has a Poisson(λ) distribution. Assume that the expected number of crossovers between two loci in a fixed period of time is 2.25.The next 3 questions refer to this model for crossovers. (The answer may be rounded up to 3 decimal places of the actual value.)

1. The probability of obtaining exactly 4 crossovers between the two loci is

2. The probability of obtaining at least 4 crossovers between the two loci is

3. A recombination between two loci occurs if the number of crossovers is odd. The probability of recombination between the two loci is, approximately, equal to ??? (Compute the probability of recombination approximately using the function "dpois". Ignore odd values larger than 9)

1.Suppose that the number of customers who enter a supermarket each hour is normally distributed with a mean of 670 and a standard deviation of 180. The supermarket is open 17 hours per day. What is the probability that the total number of customers who enter the supermarket in one day is greater than 10100? (Hint: Calculate the average hourly number of customers necessary to exceed 10100 in one 17-hour day.)

2.Assume that women's weights are normally distributed with a mean given by μ=143 lb and a standard deviation given by σ=29 lb.
(a)  If 1 woman is randomly selected, find the probabity that her weight is between 113 lb and 173 lb

(b)  If 3 women are randomly selected, find the probability that they have a mean weight between 113 lb and 173 lb

(c)  If 88 women are randomly selected, find the probability that they have a mean weight between 113 lb and 173 lb

1. The heights of an adult females are normally distributed with a mean of 150 cm and standard deviation of 8 cm. Let X be the height of an adult females;

1. Find PX ≤ 160               

2. Find P140<X<170

2. A telemarketer is a person who makes phone calls to prospective customers to promote sales of company’s products or services. The probability of a telemarketer in AZA Boutique Design in making a sale on a customer call is 0.2. Let X be the number of sale.

1. Find the probability that no sales are made in 5 calls.  

2. If the manager of the company wanted an average of 3 sales in a day, find the number of calls that should be made by a telemarketer in order to achieve the target.

3. Patients arrived at hospital emergency department follows a Poisson distribution with a mean of 4 patients per hour.

1. In any 90 minutes period of time, find the probability that exactly 10 patients arrived.                                                            

2. Find the standard deviation of the number of patients arriving at the hospital.