Refer to the data tables above and answer the following questions. Be sure to support your answers (e.g. provide probabilities, ratios, etc.).

Is there a difference in the probability of death for males vs. females?

Does age make a difference in the probability of death?

What does the number of children in relation to the number of adults tell you about this population?

Does economic status make a difference in the probability of death? Does your answer to this question differ depending on the subgroup you are looking at?

What other questions would you like to ask about these data or this event in order to help you make a determination? Can you guess what event generated this data?

According to a survey, 1.22% of factory employees in a country suffered from job related stress.

Supposed 100 employees are selected at random. We are interested to find the number of employees amongst these 100 that suffers from job-related stress.

b.(i) State the assumptions needed so that the situation can be modelled as a binomial experiment.

(ii) Hence, find the probability that at most 2 out of these 100 employees suffers from job-related stress.

(iii) Calculate the mean and standard deviation for the number of employees amongst these 100 that suffers from job-related stress.   

Suppose we are interested to use Poisson approximation for the problem in part (b).

c.(i) State the assumptions needed so that binomial distribution can be approximated by the Poisson distribution.

(ii) Assume that number of employees that suffers from job-related stress has a Poisson distribution with a mean which is equal to the mean calculated in part (b)(iii). Hence, find the probability that at most 2 of these employees suffers from job-related stress.

(iii) Compare your answer in part (c)(ii) to your answer in part (b)(ii). Is the Poisson distribution a good approximation in this case? Explain. (Note that an error of 0.005 or less would indicate a good approximation.)

(d) Suppose we are interested to use normal approximation for the problem in part (b).

(i) State the assumptions needed so that binomial distribution can be approximated by the normal distribution.

(ii) Assume that number of employees that suffers from job-related stress has a normal distribution with mean and standard deviation which are equal to the mean and standard deviation calculated in part (b)(iii). Hence, find the probability that at most 2 of these employees suffers from job-related stress.

(iii) Compare your answer in part (d)(ii) to your answer in part (b)(ii). Is the normal distribution a good approximation in this case? Explain. (Note that an error of 0.005 or less would indicate a good approximation.)

Math 473: R Homework #4 Name: Due: Thursday, November 7th at the beginning of class; if your homework is submitted at the end of class or later, it will be considered late. Please print this sheet and staple it to the front of your homework. You will not receive any credit for your program if it does not run, if you did not call the program from the R Console window, you call your program more than once from the R Console window, or your program is not done 100% in R. If you write your program line by line at the R prompt, or copy and paste it into the R prompt or submit more than one R program you will not receive any credit. You will not receive any credit for your program if your font is too small (less than 8) to be readable. You will not receive any credit if you do not use the “list” command or a command that performs the same function as “list”. See previous templates for examples. Write one R program to answer the following questions: 1. 48% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Determine the probability that the number of men who consider themselves baseball fans is exactly eight. 2. Fifty-five percent of households say they would feel secure if they had $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings. Determine the probability that the number of households that say they would feel secure is more than five. 3. 32% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Determine the probability that the number of adults who say cashews are their favorite nut is at most two. 4. 29% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Determine the probability that the number of college students who say they uses credit cards because of the rewards program is between two and five inclusive. 5. Sixty-six percent of pet owners say they consider their pet to be their best friend. You randomly select 11 pet owners and ask them if they consider their pet to be their best friend. Determine the probability that the number of pet owners who say their pet is their best friend is at least eight. Type a comment next to each line in the R program. The comments should describe what each line does. Hint: See the Probability Distributions handout on Blackboard. Hint: Use the “list” command at the end of the program (see the dice template); assign your answers to variables. Submit a printed version of the following: 1. R program 2. Program output: answers to each of the 5 questions Grade distribution: 15 points: function comments 10 points: R Console window (need to show that you compiled the function using the source command, and need to show that you called the function) 75 points: function output (print R Console screen; 15 points for the correct answer to each problem; print R Console screen).

Please i need full R program not only the out put i need the program line by line from the syntax to the out put.. thank you

A person with a cough is a persona non grata on airplanes, elevators, or at the theater. In theaters especially, the irritation level rises with each muffled explosion. According to Dr. Brian Carlin, a Pittsburgh pulmonologist, in any large audience you'll hear about 8 coughs per minute.

(a) Let r = number of coughs in a given time interval. Explain why the Poisson distribution would be a good choice for the probability distribution of r.

Coughs are a common occurrence. It is reasonable to assume the events are dependent.Coughs are a common occurrence. It is reasonable to assume the events are independent.    Coughs are a rare occurrence. It is reasonable to assume the events are dependent.Coughs are a rare occurrence. It is reasonable to assume the events are independent.

(b) Find the probability of six or fewer coughs (in a large auditorium) in a 1-minute period. (Use 4 decimal places.)


(c) Find the probability of at least eight coughs (in a large auditorium) in a 24-second period. (Use 4 decimal places.)

Customers arrive at a local grocery store at an average rate of 2 per minute.

(a) What is the chance that no customer will arrive at the store during a given two minute period?

(b) Since it is a “Double Coupon” day at the store, approximately 70% of the customers coming to the store carry coupons. What is the probability that during a given two-minute period there are exactly four (4) customers with coupons and one (1) without coupons?

(c) Divide one given hour into 30 two-minute periods. Suppose that the numbers of customers arriving at the store during those periods are independent of each other. Denote by X the number of the periods during which exactly 5 customers arrive at the store and 4 of them carry coupons. What is the probability that X is at least 2?

(d) What is the probability that exact 4 customers coming to the store during a given two-minute period carry coupons?

A recent study shows that on average 21% of employees in the work population prefer their vacation time during March break. Vincent Company employs 55 people. Use the normal approximation to the binomial distribution to answer the questions below:

Required:

1. Determine the expected value, and the standard deviation of that value, of the number of Vincent Company employees who would prefer their vacation time during March break. 
2. What is the probability that more than nine Vincent Company employees will prefer their vacation during March break? Sketch a normal curve and shade the desired area of your diagram. 
3. What is the probability that exactly nine Vincent Company employees will prefer their vacation during March break? Sketch a normal curve and shade the desired area of your diagram.  
4. What is the probability that more than six, but less than ten, Vincent Company employees will prefer their vacation during March break? Sketch a normal curve and shade the desired area of your diagram. 

4. (a) Susan tries to exercise at ”Pure Fit” Gym each day of the week, except on the weekends (Saturdays and Sundays). Susan is able to exercise, on average, on 75% of the weekdays (Monday to Friday).

1. Find the expected value and the standard deviation of the number of days she exercises in a given week.    [2 marks]
2. Given that Susan exercises on Monday, find the probability that she will exercise at least 3 days in the rest of the week. [3 marks]
3. Find the probability that in a period of four weeks, Susan exercises 3 or less days in only two of the four weeks.      [3 marks]

2. A car repair shop uses a particular spare part at an average rate of 6 per week. Find the probability that:
   1. at least 6 are used in a particular week.                                                            [2 marks]
   2. exactly 18 are used in a 3-week period.                                                             [3 marks]
   3. exactly 6 are used in each of 3 successive weeks.

PLZ ans 4B

Assume that the Gamecocks basketball team has a probability of 0.70 of winning a game against any opponent, and that the outcomes of its games are independent of each other. Suppose during the basketball season it will play a total of 30 games. Let X denote the total number of games that it will win during the season.

(a) Write down the formula for the probability mass function (pmf) (p(x)) of X. Is your pmf the binomial pmf?

(b) Use a computer (R will be good to use) or calculator to compute p(x) for each x = 0, 1, 2, . . . , 30. Then plot these probabilities with respect to x. Describe the shape of this PMF.

(c) Find Pr{X ≥ 25}.

(d) Find Pr{15 < X ≤ 20}.

(e) Find the mean µ of X.

(f) Find the variance σ 2 and standard deviation σ of X.

(g) Compute Pr{µ − 2σ ≤ X ≤ µ + 2σ}. Is this probability close to 0.95?

Many human diseases are genetically transmitted (for example, hemophilia or Tay-Sachs disease). Here is a simple model for such a disease. The genotype aa is diseased and dies before it mates. The genotype Aa is a carrier but is not diseased. The genotype AA is not a carrier and is not diseased.

a. If two carriers mate, what are the probabilities that their offspring are of each of the three genotypes?

b. If the male offspring of two carriers is not diseased, what is the probability that he is a carrier?

c. Suppose that the non-diseased off spring of part (b) mates with a member of the population for whom no family history is available and who is thus assumed to have probability p of being a carrier ( p is a very small number). What are the probabilities that their first offspring has the genotypes AA, Aa, and aa?

d. Suppose that the first offspring of part (c) is not diseased. What is the probability that the father is a carrier in light of this evidence?

DO NOT COPY PASTE CHEGG ANSWERS BACK HERE thanks

Commemorative coins are being struck at the local foundry. A gold blank (a solid gold disc with no markings on it) is inserted into a hydraulic press and the obverse design is pressed onto one side of the disc (this step fails with probability 0.15). The work is examined and if the obverse pressing is good, the coin is put into a second hydraulic press and the reverse design is imprinted (this step fails with probability 0.08). The completed coin is now examined and if of sufficient quality is passed on for finishing (cleaning, buffing, and so on). Twenty gold blanks are going to undergo pressing for this commemorative coin. Assume that all pressings are independent of each other.

Part 4a: What are the mean and variance of the number of good coins manufactured?

Part 4b: If the blanks cost $300 each and the labor to produce the finished coins costs $3,000, what is the probability that the production cost to make the 20 coins (labor and materials) can be recovered by selling the coins for $500 each?