Given a standard deck of cards, find the following:
a) ?(7 of spades | black card)
b) The probability that the first card is red and the second is the King of Clubs (this is a black card)
c) The probability that the first card is the King of Clubs and the second is red
d) What is the probability of drawing 3 kings when drawing 3 cards?

High school girls average 80 text messages daily. Assume the population standard deviation is 15 text messages. Assume normality.

1. What is the probability that the sample mean is more than 90?
2. What is the probability that the sample mean is less than 85?
3. What is the probability the sample mean is in between 85 and 90?

of the three men, the chances that of politician, a businessman, of an academician will be appointed as a vice-chancellor (vc) of a university are 0.5,0.3 and 0.2 respectively. Probability that the research is promoted to become vc of the university politician, businessman, and academician 0.3, 0.7, and 0.8 respectively. a) determine the probability that research is promoted. b) if reserch is promoted, what is the probability that vc is and academician?

A) If four babies are born in a given hospital on the same day, what is the probability that all four will be boys?
B) if four babies are born in a given hospital on the same day, what is the probability that 3 will be girls and 1 will be a boy?
C) You flip a coin twice what is the probability that it lands on heads once and tails one?

A consumer advocate claims that 75 percent of cable television subscribers are not satisfied with their cable service. In an attempt to justify this claim, a randomly selected sample of cable subscribers will be polled on this issue.

(a) Suppose that the advocate's claim is true, and suppose that a random sample of 5 cable subscribers is selected. Assuming independence, use an appropriate formula to compute the probability that 4 or more subscribers in the sample are not satisfied with their service. (Do not round intermediate calculations. Round final answer to p in 2 decimal place. Round other final answers to 4 decimal places.)

A consumer advocate claims that 75 percent of cable television subscribers are not satisfied with their cable service. In an attempt to justify this claim, a randomly selected sample of cable subscribers will be polled on this issue.

(a) Suppose that the advocate's claim is true, and suppose that a random sample of 5 cable subscribers is selected. Assuming independence, use an appropriate formula to compute the probability that 4 or more subscribers in the sample are not satisfied with their service. (Do not round intermediate calculations. Round final answer to p in 2 decimal place. Round other final answers to 4 decimal places.)

(b) Suppose that the advocate's claim is true, and suppose that a random sample of 20 cable subscribers is selected. Assuming independence, find: (Do not round intermediate calculations. Round final answer to p in 2 decimal place. Round other final answers to 4 decimal places.)

Binomial, n =_________ , p = ___________

1. The probability that 10 or fewer subscribers in the sample are not satisfied with their service.

Probability             

2. The probability that more than 15 subscribers in the sample are not satisfied with their service.

Probability ___________   

3. The probability that between 15 and 18 (inclusive) subscribers in the sample are not satisfied with their service.

Probability __________

4. The probability that exactly 18 subscribers in the sample are not satisfied with their service.

Probability _______________

(c) Suppose that when we survey 20 randomly selected cable television subscribers, we find that 10 are actually not satisfied with their service. Using a probability you found in this exercise as the basis for your answer, do you believe the consumer advocate's claim? Explain. (Round your answer to 4 decimal places.)

(Click to select)  Yes  No  ; if the claim is true, the probability that 10 or fewer  (Click to select)  are  are not  satisfied is only  .

A statistics class for engineers consists of 53 students. The students in the class are classified based on their college major and sex as shown in the following contingency table:

If a student is selected at random from the class by the instructor to answer a question, find the following probabilities. Report your answer to 4 decimal places. (total 80 points)

Consider the following events:

A: The selected student is a male.

B: The selected student is industrial engineering major.

C: The selected student is civil engineering major.

D: The selected student is electrical engineering major.

Note: Indicate the type of probability as marginal, joint or conditional when asked.

Find the probability that the randomly selected student is a male. Indicate the type of probability. (8 + 2 = 10 points)

Find the probability that the randomly selected student is industrial engineering major. Indicate the type of probability. (8 + 2 = 10 points)

Find the probability that the randomly selected student is male industrial engineering major. Indicate the type of probability. (8 + 2 = 10 points)

Given that the selected student is industrial engineering major, what is the probability that the student is male? Indicate the type of probability.

(8 + 2 = 10 points)

Based on your answers on part a and d, are sex and college major of students in this class independent? Provide a mathematical argument? (6 points)

Consider the events A and B. Are sex and college major mutually exclusive events? Provide a mathematical argument to justify your answer. (6 points)

Find the probability that the randomly selected student is male or industrial engineering college major. (10 points)

Consider the events C and D. Are college major mutually exclusive events? Provide a mathematical argument to justify your answer. (6 points)

Find the probability that the randomly selected student is civil or electrical engineering college major. (6 points)

What is the probability that a randomly selected student is neither a male nor an industrial engineering college major? (6 points)

1.   Describe what type of data analysis would use linear correlation coefficients and line of best fits. Describe the benefits of comparing to a line of best fit. (10 points)

2. Raw data is found in the excel file titled “STA322 Week 3 Data – Tab Line of Best Fit.” Calculate the linear correlation coefficient of that data and describe what that information provides. Find the slope and y intercept and list the line of best fit. Take Microsoft Excel and graph this line of best fit, using the “trend” function. Determine how you will implement the results you received to improve the data, base it on a scenario for your career. (30 points)

3. Express the likelihood given as a probability between 0 and 1 for the following (20 points):

                a. The Weather Channel stated that we have a 75% chance of being hit by the hurricane.

                b. I have a 22% chance of winning the Sweepstakes.

                c. When playing Yahtzee, I can roll 1 die and I need a 4. What are my chances?

                d. The gender of the new baby being a girl.

4. A survey was taken at a K-6^th grade school. Do you have enough time at lunch? Given the table below, answer the following questions (20 points):

If b represents the event of selecting a response from a boy, find P(Ђ).

Find the probability that the selected answer was made by a girl or was answered no.

If g represents the event of selecting a response from a girl, find P (ḡ).

Find the probability that the selected answer was made by a boy and answered yes.

5. Find the number of ways that 6 Discussion responses can be ordered by calculating 6! (5 points)

6. Find the number of ways that the 5 children can line up to go to recess by calculating 5! (5points)

Use Permutations or Combinations on the next 3 examples:

7. If you are allowed to use numbers 1 – 20 and need to choose the passcode of an exact 4 digit code, how many possibilities are there? (10 points)

8. If there are 25 students in the class and we need to select a President and Secretary for our meetings, how many possibilities are there? (10 points)

9. In playing a card game, I am dealt 6 cards, how many possibilities are there for my hand? (10 points)

For 11 trials that follow a binomial distribution with the probability of failure at 6%. Find the probability of exactly 7 success Using a calculator.

What are the requirements for a probability distribution? Differentiate between a discrete and a continuous random variable. Discuss the requirements for a binomial probability experiment.

Suppose you play a coin toss game in which you win​ $1 if a head appears and lose​ $1 if a tail appears. In the first 100 coin​ tosses, heads comes up 34 times and tails comes up 66 times. Answer parts​ (a) through​ (d) below. a. What percentage of times has heads come up in the first 100​ tosses? 34​% What is your net gain or loss at this​ point? Select the correct choice and fill in the answer box to complete your choice. A. You have lost ​$ 32. ​(Type an​ integer.) B. You have gained ​$ nothing. ​(Type an​ integer.) b. Suppose you toss the coin 200 more times​ (a total of 300​ tosses), and at that point heads has come up 37​% of the time. Is this change in the percentage of heads consistent with the law of large​ numbers? Explain. A. The change is consistent with the law of large numbers​ because, as the number of trials​ increases, the proportion should grow closer to​ 50%. B. The change is consistent with the law of large numbers. Because the percentage is low the first 100​ trials, it has to be higher the next 200 trials to even out. C. The change is not consistent with the law of large numbers​ because, as the number of trials​ increases, the proportion should grow closer to​ 50%. D. The change is not consistent with the law of large​ numbers, because the trials are not independent. What is your net gain or loss at this​ point? Select the correct choice and fill in the answer box to complete your choice. A. You have gained ​$ nothing. ​(Type an​ integer.) B. You have lost ​$ nothing. ​(Type an​ integer.) c. How many heads would you need in the next 100 tosses in order to break even after 400​ tosses? Is this likely to​ occur? Select the correct choice and fill in the answer box to complete your choice. A. You would need to toss nothing heads. This is likely because so few heads have been tossed so far. B. You would need to toss nothing heads. This is unlikely as it is far from the expected number of heads. C. You would need to toss nothing heads. This is likely because it is close to the expected number of heads. d. Suppose​ that, still behind after 400​ tosses, you decide to keep playing because you are due for a winning streak. Explain how this belief would illustrate the​ gambler's fallacy. A. This illustrates the​ gambler's fallacy because eventually there will be a winning streak. B. This illustrates the​ gambler's fallacy​ because, due to the law of large​ numbers, the probability of getting heads must now be more than 0.5. C. This illustrates the​ gambler's fallacy because the number of heads cannot be under​ 50% all the time. D. This illustrates the​ gambler's fallacy because the probability of getting heads is always 0.5.