State Farm Insurance studies show that in Colorado, 50% of the auto insurance claims submitted for property damage were submitted by males under 25 years of age. Suppose 8 property damage claims involving automobiles are selected at random.

(a) Let r be the number of claims made by males under age 25. Make a histogram for the r-distribution probabilities. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot

(b) What is the probability that seven or more claims are made by males under age 25? (Use 3 decimal places.) (c) What is the expected number of claims made by males under age 25? What is the standard deviation of the r-probability distribution? (Use 2 decimal places.) μ σ

State Farm Insurance studies show that in Colorado, 65% of the auto insurance claims submitted for property damage were submitted by males under 25 years of age. Suppose 10 property damage claims involving automobiles are selected at random. (a) Let r be the number of claims made by males under age 25. Make a histogram for the r-distribution probabilities. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot

(b) What is the probability that six or more claims are made by males under age 25?

(Use 3 decimal places.) (c) What is the expected number of claims made by males under age 25? What is the standard deviation of the r-probability distribution? (Use 2 decimal places.) μ σ Need Help?

1. A recruiter, Joey Falcon, interviews 6 students. Each student has a probability of 0.2 of receiving a recommendation from Joey Falcon (the result from each student is independent from the results of the other students). Let X be the number students who Joey Falcon recommends.

A second recruiter, Sophie Secaucus, interviews 4 students (different from the above 6 students). Each student has a probability of 0.3 of receiving a recommendation from Sophie Secaucus (the result from each student is independent from the results of the other students. Let Y be the number of students who Sophie Secaucus recommends.

1. Find the joint pmf for X,Y (assume X and Y are independent).
2. Find p(X<3, Y<2)
3. Find p(X+Y<5)

In the 2004 baseball season, Ichiro Suzuki of the Seattle Mariners set the record for most hits in a season with a total of 262 hits. In the following probability distribution, the random variable X represents the number of hits Ichiro obtained in a game.

1. What is the probability that in a randomly selected game, Ichiro got at least 3 hits? =.2112
2. Compute the mean of the random variable X. (round to two decimal places) =1.63
3. Compute the standard variation of the random variable X. (round to two decimal places) =1.18

4) What would be the upper limit of range that would include the number of hits Ichiro obtained in 75% of the games?

1. About 1% of the population has a particular genetic mutation. 200 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 200.

2. A drug test is accurate 97% of the time. If the test is given to 1600 people who have not taken drugs, what is the probability that at least 50 will test positive?

Probability =

Give your answers to at least 3 decimal places.

3. According to the American Red Cross, 9.4% of all Connecticut residents have Type B blood. A random sample of 23 Connecticut residents is taken.

X=X=the number of CT residents that have Type B blood, of the 23 sampled.

What is the standard deviation of the random variable XX?

Suppose my grocery store of choice has 20 shopping carts in total and 10 of them have wobbly wheels (they don’t really push properly). I’ve gone to the store with 3 of my friends to stock up for a big party and we decide to split up (each of us taking a cart, so 4 carts in total). Let X be the number of carts with wobbly wheels (out of the 4 me and my friends have taken).What is the distribution of X?Give the name of the distribution and the appropriate parameters.What is the mean and variance of this distribution? Give your answer as a number,but include the formulas (or logic) used.

What is the probability exactly 2 of us have carts with wobbly wheels?

What is the probability that at least 1 of us has a cart with wobbly wheels?

Question 8: Let’s say an interviewer wants to select 2 people at random of 3. The three individuals are Sally, Joe, John.

1. a.) List the sample space of this experiment (that is make all possible outcomes that can happen in this situation).
2. b.) Given each event in the sample space is equally likely, find each probability .
3. c.) What is the probability of selecting Joe in this interview?

Question 9: Please answer the following questions and determine if this represents a discrete random variable or a continuous random variable.

1. a.) The number of inches it rains per day in the state of Washington. Does this represent a discrete or continuous random variable? Why or why not.
2. b.) The number of times of getting heads after flipping a coin 20 times. Does this represent a discrete or continuous random variable? Why or why not.

A hat contains a number of cubes: 3 red, 2 white, 1 blue, and 4 black.

1. If one cube is chosen at random, what is the probability that it is:

1. A red cube? (3 points)
2. Not a red cube? (3 points)
3. A cube that is white OR black? (4 points)
4. A cube that is neither white nor black? (4 points)
5. What do the answers to part a and part b add up to and why? (5 points)

2. If three cubes are chosen at random, with replacement, what is the probability that:

1. All three cubes are white? (4 points)
2. None of the cubes are white? (4 points)
3. At least one of the cubes is white? (4 points)
4. The first cube is red, and the next two are black (4 points)

3. Explain how you could simulate this experiment using a random number table. (5 points)