Q1
In a class on 50 students, 35 students passed in all subjects, 5 failed in one subject, 4 failed in two subjects and 6 failed in three subjects.

Construct a probability distribution table for number of subjects a student from the given class has failed in.
Calculate the Standard Deviation.








Q2
45 % of the employees in a company take public transportation daily to go to work. For a random sample of 7 employees, what is the probability that at most 2 employees take public transportation to work daily?

















               
     Q3. Find
        a) P(z < 1.87)
        b) P(z > -1.01)
        c)   P(-1.01 < z < 1.87)
           






Q4
Assume the population of weights of men is normally distributed with a mean of 175 lb. and a standard deviation 30 lb. Find the probability that 20 randomly selected men will have a mean weight that is greater than 178 lb.



















   
Q5
We have a random sample of 100 students and 75 of these people have a weight less than 80 kg. Construct a 95% confidence interval for the population proportion of people who have a weight less than 80 kg.










Q6
We have a sample of size n = 20 with mean x ̅ =12 and the standard deviation σ=2. What is a 95% confidence interval based on this sample?

John is lying on the sidewalk after robbing a bank, in pain and mulling over how to quantify the uncertainty of his survival, when Dirty Harry walks over. Dirty Harry pulls out his 44 Magnum and puts two bullets opposite each other in the six slots in the cylinder (e.g., if you number them 1 .. 6 clockwise, he puts them in 1 and 4), spins the cylinder randomly, and, saying "The question is, are you feeling lucky, probabalistically speaking, computer science punk?" points it at John head and pulls the trigger.... "CLICK!" goes the gun (no bullet) and Dirty Harry smiles... "How about that .... Let's see if this gun is memory-less!" Without spinning the cylinder again, he points the gun at Wayne's head and pulls the trigger again.

(a) What is the probability that (at least in my dream) John is hit?

(b) Now, suppose that when Dirty Harry put the bullets in the gun, he put them right next to each other (e.g., in slots 1 and 2). He spins it as usual. What is the probability in this case John is hit?

(c) Suppose Dirty Harry puts the bullets in two random positions in the cylinder and we don't have any idea where they are. He spins it as usual. Now what is the probability that John will be hit?

You may need to use the appropriate appendix table or technology to answer this question.

According to the National Association of Colleges and Employers, the 2015 mean starting salary for new college graduates in health sciences was $51,541. The mean 2015 starting salary for new college graduates in business was $53,901. † Assume that starting salaries are normally distributed and that the standard deviation for starting salaries for new college graduates in health sciences is $11,000. Assume that the standard deviation for starting salaries for new college graduates in business is $17,000.

(a)

What is the probability that a new college graduate in business will earn a starting salary of at least $65,000? (Round your answer to four decimal places.)

(b)

What is the probability that a new college graduate in health sciences will earn a starting salary of at least $65,000? (Round your answer to four decimal places.)

(c)

What is the probability that a new college graduate in health sciences will earn a starting salary less than $46,000? (Round your answer to four decimal places.)

(d)

How much would a new college graduate in business have to earn in dollars in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences? (Round your answer to the nearest whole number.)

$

A(n)10.0?%,?25-yearbond has a par value of? $1,000and a call price of ?$1,125. ?(Thebond's first call date is in 5? years.)Coupon payments are made semiannually? (souse semiannual compounding where appropriate).

a. Find the current? yield,YTM, and YTC on this? issue,given that it is currently being priced in the market at $1,250. Which of these 3 yields is the? highest?Which is the? lowest?Which yield would you use to value this? bond?Explain.

b.Repeat the 3 calculations? above,given that the bond is being priced at ?$900. Now which yield is the? highest?Which is the? lowest?Which yield would you use to value this? bond?Explain.

A.If the bond is priced at $1250? the current yield is -----------?%.?(Roundto two decimal? places.)

The annual? yield-to-maturitywith semiannual compounding is -------?%.?(Roundto two decimal? places.)

The annual? yield-to-callwith semiannual compounding is ----------?%. (Roundto two decimal? places.)

Which of these 3 yields is the? highest?------------Which is the? lowest? ---------

Which yield would you use to value this? bond? ?(Selectthe best answer? below.)

A. The? yield-to-maturityis always used.

B. The? yield-to-maturitybecause convention is to use the lower of? yield-to-maturityor? yield-to-callfor bonds selling at a discount.

C. The? yield-to-maturitybecause the bonds may not be called.

D. It? doesn'tmatter which yield you use.

B. If the bond is priced at $900?,the current yield is---------------?%.?(Roundto two decimal? places.)

The annual? yield-to-maturitywith semiannual compounding is --------------?%.?(Roundto two decimal? places.)

The annual? yield-to-callwith semiannual compounding is ------------?%.?(Roundto two decimal? places.)

Which of these 3 yields is the? highest?Which is the? lowest????(Selectfrom the? drop-downmenus.)

Current yield

Yield-to-maturity

Yield-to-call

Which yield would you use to value this? bond??

?A. It? doesn'tmatter which yield you use.

B. The? yield-to-maturitybecause the bonds may not be called.

C. The? yield-to-maturitybecause convention is to use the lower of? yield-to-maturityor? yield-to-callfor bonds selling at a discount.

D.The? yield-to-maturityis always used.

1. When identical parts are being manufactured. They vary from one another. If the variation is normally distributed if:

a) is natural and is to be expected

b) indicates the parts do not meet quality standards

c) indicates an unstable process is developing

2. Probability tells us:

a) how often something actually occurs

b) how often something is expected to occur

c) the number of random samples it takes for an event to occur

3. Unnatural variation is normally the result of:

a) expected variation in the process

b) assignable causes

c) product design choices

4. A histogram is a graph of:

a) the past history of the process

b) machine capability

c) how often events or measurements occur

5. The normal distribution curve:

a) is a picture of how products are distributed from a stable set of conditions

b) provides accurate information about specification limits

c) allows us to identify causes of variation

6. The mean of a sample taken from a population:

a) is written as x

b) is the result of measuring all the individuals

c) determines process capability

7. Range is:

a) the number of times an event occurs

b) the difference between highest and lowest values

c) shown on an x chart

8. The variability of a group is described by:

a) standard deviation

b) population totals

c) the value between the first and last piece produced

9. A “quality” product is one that:

a) is within the specification limits

b) meets the needs and expectations of the customer

c. uses geometric dimensioning and tolerancing

10. Statistical Process Control:

a) tracks the variability of products or services

b) will solve he majority of quality related problems

c) is most useful during 100% inspection

11. The normal distribution of average is:

a) larger than the distribution of individuals

b) narrower than the distribution of individuals

c) the same as the distribution of individuals

12) A product’s key quality characteristics are monitored:

a) during final inspection

b) within +- 0.001

c) using control chart

13. Control limits on an x are:

a) the statistical words for blueprint tolerances

b) based upon the distribution of sample averages

c) used to determine process capability

14) Process capability studies:

a. given information about how a process is behaving

b) are most effective in determining whether or not SPC works

c) require that a single machine be capable of producing at least 2 different parts

15) Values plotted as points on an x chart are:

a) individual values

b) specification limits

c) sample values

16. The pattern of points on an x chart should show a normal distribution that:

a) closely parallels individual measurement

b) shows percent defective

c) is within +- 3 sigma

1 (a) If 14 women compete in the marathon at the Olympics, in how many different ways can the gold, silver and bronze medals be awarded?

(b) If a three person committee is chosen at random from a group of 15 people, how many different committees are possible?

(c) In a new lottery game called "Minibucks", you select four numbers between 1 and 28. If you match all four numbers with the four numbers chosen by the lottery that day, you win the jackpot. (It doesn't matter whether the order that the lottery selected the numbers matches the order that you selected the numbers). What is the minimum number of different Minibucks tickets you would need to buy for one drawing in order to be 100% certain to win the jackpot for that drawing?

(d) In a new lottery game called "Minibucks version 2", you select four numbers between 1 and 25. If you match exactly three of your numbers with the four numbers chosen by the lottery that day, you win $5. What is the probability that you win this prize? Write your answer as a decimal accurate to four decimal places.

(e) A drawer contains 16 white socks and 6 black socks. Two different socks are selected from the drawer at random. What is the probability that both of the selected socks are white? Write your answer as a decimal accurate to three decimal places.

(f) According to https://www.cologuardtest.com/meet-cologuard/how-effective-is-cologuard (Links to an external site.) , if a person with colon cancer is given a Cologuard test, the probability that colon cancer is diagnosed by the test is 92%. If a person without colon cancer is given a Cologuard test, the probability that colon cancer is incorrectly diagnosed by the test is 13%. (This means that the probability of a false positive test result is 13%, and the test is said to have 87% specificity). Suppose that 2.5 % of the population actually has colon cancer. If a person is diagnosed as having colon cancer based on a Cologuard test, what is the probability that the person actually has colon cancer? Write your answer as a decimal accurate to three decimal places.

CNNBC recently reported that the mean annual cost of auto insurance is 967 dollars. Assume the standard deviation is 291 dollars. You take a simple random sample of 92 auto insurance policies.

A. Find the probability that a single randomly selected value is less than 984 dollars.
P(X < 984) =

Find the probability that a sample of size n=92 is randomly selected with a mean less than 984 dollars.
P(M < 984) =

Enter your answers as numbers accurate to 4 decimal places.

B. A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 23 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 23 weeks and that the population standard deviation is 4 weeks. Suppose you would like to select a random sample of 72 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is greater than 24.1.
P(X > 24.1) =  

(Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a sample of size n=72 is randomly selected with a mean greater than 24.1.
P(M > 24.1) =

(Enter your answers as numbers accurate to 4 decimal places.)

C. Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 155000 dollars. Assume the standard deviation is 45000 dollars. Suppose you take a simple random sample of 57 graduates.

Find the probability that a single randomly selected policy has a mean value between 135330.7 and 177649.5 dollars.
P(135330.7 < X < 177649.5) =  

(Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a random sample of size n=57 has a mean value between 135330.7 and 177649.5 dollars.
P(135330.7 < M < 177649.5) =  

(Enter your answers as numbers accurate to 4 decimal places.)

a) A type of battery-operated led lights has a known mean lifetime 7.8 hrs with standard deviation 0.5. It's provided that the lifetimes of these led lights are normally distributed. Without using the LSND program, find the probability that one of these led lights, selected at random, having lifetime between 6.8 and 7.8 hours.

b) According to a medical study, it takes about 48 hrs, on average, for Roseola virus to fade away in infected patients (children). Assuming that the fading times of Roseola virus in infected patients are normally distributed with standard deviation 0.7, what's the probability of having a random case where the fading time of the virus in an infected patient is less than 48 hours? Find the answer without using the LSND program.

c) pH measurements of a chemical solutions have mean 6.8 with standard deviation 0.04. Assuming all pH measurements of this solution follow a normal distribution, find the probability of selecting a pH measurement at random that reads below 6.68 OR above 6.88 without using the LSND program.

d) Salaries for senior Civil engineers per year have known mean of 72 K dollars and standard deviation 3.3 K dollars. Provided that the salaries per year for senior Civil engineers are normally distributed, what's the probability of finding a Civil engineer whose salary is between 68.7 K and 81.9 K dollars? Find the answer without using the LSND program.

e) Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are normally distributed, with a mean of 4.4 millimeters (mm) and a standard deviation of 1 mm. What's the probability that an ancient prehistoric Native American pot shard discovered in this area has thickness measurement thicker than 4.4? Find the answer without using the LSND program.

f)  scores in a Math class with large number of students have mean 147 and standard deviation 7.5. Provided the scores of this scores follow a normal distribution, what's the probability that a student scores below 154.5 OR above 162? Find the answer without using the LSND program.

May I have the answers for the following questions step by step please.

1. Annual sales, in millions of euros, for 21 pharmaceutical companies follow.

          8408               1374               1872               8879               2459               11413             608

14138 6452 1850 2818 1356 10498 7478

4019 4341 739 2127 3653 5794 8305

1. Provide a five-number summary.
2. Compute the lower and upper limits for the box plot.

2. Suppose that IQ scores have a bell-shaped distribution with a mean of 100 and a standard deviation of

15.

1. What percentage of people have an IQ score between 85 and 115?
2. What percentage of people have an IQ score between 70 and 130?
3. What percentage of people have an IQ score of more than 130?
4. A person with an IQ score greater than 145 is considered a genius. Does the empirical rule support this statement? Explain.

3. A sample has data values 27, 25, 20, 15, 30, 34, 28, 25. Calculate the range, interquartile range, variance, standard deviation and coefficient of variation.

4. Use the below table to answer the questions:

1. What is the probability that the victim has fatalities?
2. What is the probability that the victim was an adult and he/she has serious injuries?
3. What is the probability that the victim was a child or he/she has fatalities?
4. What is the probability of a serious injury given the victim was a child?
5. What is the probability that the victim was an adult given a fatality occurred?

5. A company is about to sell to a new client. It knows from past experience that there is a real possibility that the client may default on payment. As a precaution the company checks with a consultant on the likelihood of the client defaulting in this case and is given an estimate of 20%. Sometimes the consultant gets it wrong. Your own experience of the consultant is that he is correct 70% of the time when he predicts that the client will default but that 20% of clients who he believes will not default actually do. What is the probability that the new client will not default?

A restaurant manager is interested in taking a more statistical approach to predicting customer load. She begins the process by gathering data. One of the restaurant hosts or hostesses is assigned to count customers every five minutes from 7 P.M. until 8 P.M. every Saturday night for three weeks. The data are shown here. After the data are gathered, the manager computes lambda using the data from all three weeks as one data set as a basis for probability analysis.What value of lambda did she find? Assume that these customers randomly arrive and that the arrivals are Poisson distributed. Use the value of lambda computed by the manager and help the manager calculate the probabilities in parts (a) through (e) for any given five-minute interval between 7 P.M. and 8 P.M. on Saturday night. Number of Arrivals Week 1 Week 2 Week 3 3 1 5 6 2 3 4 4 5 6 0 3 2 2 5 3 6 4 1 5 7 5 4 3 1 2 4 0 5 8 3 3 1 3 4 3 a. What is the probability that no customers arrive during any given five-minute interval? b. What is the probability that five or more customers arrive during any given five-minute interval? c. What is the probability that during a 10-minute interval fewer than four customers arrive? d. What is the probability that between four and six (inclusive) customers arrive in any 10-minute interval? e. What is the probability that exactly six customers arrive in any 15-minute interval? *Round your answers to 4 decimal places when calculating using Table A.3. **Round your answer to 4 decimal places, the tolerance is +/-0.0005. a. P(x = 0) = * b. P(x ≥ 5) = * c. P(x < 4 | 10 minutes) = * d. P(4 ≤ x ≤ 6 | 10 minutes) = * e. P(x = 6 | 15 minutes) = **