A student is taking a quiz with nine questions. Each question has answers: A, B, C, or D. The student guesses on each question
     
      a) how many repetitions for this problem?
      b) what is the probability of success on the 1st repetition?
   c) what is the probability of guessing 3 answers correctly?

d) what is the probability of guessing at most 2 correct?

Assume a normal distribution for each question.

(a) What proportion of the distribution consists of z-scores greater than 0.25? (

b) What is the probability of obtaining a z-score less than 0.50? (

c) What is the probability of obtaining a z-score greater than −1.50?

(d) What is the probability of obtaining a z-score between +1.00 and −1.00?

A 3-person jury has 2 members each of whom have independently a probability 0.7 of making a correct decision. The third juror just flips a coin for each decision. In this jury, the majority rules. A 1-person jury has a probability 0.7 of making a correct decision. What is the probability of the best jury of making a correct decision?

Post a clear and logical response in 150 to 200 words to the following questions/prompts, providing specific examples to support your answers.

Think about examples of how using probability distribution could affect ethics. What are the ethical concerns with capitalizing using probability distribution techniques? Provide an example of using probability distribution techniques.

To navigate on Lake Latte (fed by the Decaf and the Vanilla Rivers) at least two of the three
radio navigation beacons must be working. If the probability that a beacon is working is
p and the operational status of each station is independent of the other two, what is the
probability of being able to navigate on the lake? What is the probability that beacon #2 is
working if navigation on the lake is possible?

Consider an m-member jury that requires n or more votes to convict a defendant. Let p be the probability that a juror votes a guilty person innocent and let q be the probability that a juror votes an innocent person guilty, 0<p<1, 0<q<1. Assuming that r is the fraction of guilty defendants and that jurors vote independently, what is

(a) the probability a defendant is convicted?

(b) the probability a defendant is convicted when n=9, m=12, p=.25, q=.2, and r=5/6? Use R to calculate the result.

It has been determined that an agent of S.H.I.E.L.D. spends an average of 108 days per year identifying potential threats to human existence, with a standard deviation of 13.5 days. A random sample of 36 S.H.I.E.L.D. agents is taken.

a. What is the probability that the sample will have a mean of less than 105 days?

b. What is the probability that the sample will have a mean of more than 110 days?

c. What is the probability that the sample will have a mean between 109 and 114 days?

d. What is the probability that the sample will have a mean of no more than 104 days?

A bucket contains exactly 3 marbles, one red, one blue and one green.

A person arbitrarily pulls out each marble one at a time.

Given the following:

• Event 1: The first marble removed is non-red
• Event 2: The last marble removed is non-red

Which of the following statements is NOT true?

A.The probability of both events happening is 50%.

B.The probability of either of these events happening is 33%.

C.Event 1 is independent of Event 2.

D.The probability of Event 1 occurring is the same as the probability of Event 2 occurring.

The population mean and standard deviation are given below. Find the indicated probability and determine whether a sample mean in the given range below would be considered unusual. If​ convenient, use technology to find the probability. For a sample of nequals=3737​, find the probability of a sample mean being less than 12 comma 75212,752 or greater than 12 comma 75512,755 when muμequals=12 comma 75212,752 and sigmaσequals=1.31.3. For the given​ sample, the probability of a sample mean being less than 12 comma 75212,752 or greater than 12 comma 75512,755 is

3)   Scores on the SAT are normally distributed with a mean of 500 and a standard deviation of 100

1. What is the probability of obtaining a score greater than 640?
2. What is the probability of obtaining a score less than 390?
3. What is the probability of obtaining a score between 725 and 800?
4. What is the probability of obtaining a score either less than 375 or greater than 650?

4) If you obtained a score of 75 on an test, the standard deviation was 12 and you were told you had a score higher than 80 percent of your classmates, what was the mean on the test?