a ball is thrown vertically upward with a speed of 8.0 m/s (a) How high does it rise? (b) how long does it take to reach its highest point? (c) How long does it take to hit the ball to take to hit the ground after it reaches its highest point? (d) What is its velocity when it returns to the level from which it started?

3 men and 7 women are ranked according to their scores on an exam. Assume that no two scores are alike, and that all 10! possible rankings are equally likely. Let X denote the highest ranking achieved by a man (so X=1 indicates that a man achieved the highest score on the exam). Find each of the following:
P(X=2)=
P(X=6)=
P(X=7)=

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 340 grams and a standard deviation of 11 grams. Find the weight that corresponds to each event. (Use Excel or Appendix C to calculate the z-value. Round your final answers to 2 decimal places.)

highest 30 percent

middle 70 percent

highest 90 percent

lowest 20 percent

A 0.408 kg pendulum bob passes through the lowest part of its path at a speed of 2.71 m/s. What is the tension in the pendulum cable at this point if the pendulum is 86.8 cm long? A.) When the pendulum reaches its highest point, what angle does the cable make with the vertical? B.) What is the tension in the pendulum cable when the pendulum reaches its highest point?

Marie distributes toys for toddlers. She makes visits to households and gives away one toy only on visits for which the door is answered and a toddler is in residence. On any visit, the probability of the door being answered is 3/4, and the probability that there is a toddler in residence is 1/3. Assume that the events “Door answered" and “Toddler in residence" are independent and also that events related to different households are independent.

What is the probability that she has not distributed any toys by the end of her second visit?

What is the probability that she gives away the first toy on her fourth visit?

Given that she has given away her second toy on her fifth visit, what is the conditional probability that she will give away her third toy on her eighth visit?

What is the probability that she will give away the second toy on her fourth visit?

Given that she has not given away her second toy by her third visit, what is the conditional probability that she will give away her second toy on her fifth visit?

We will say that Marie “needs a new supply"" immediately after the visit on which she gives away her last toy. If she starts out with three toys, what is the probability that she completes at least five visits before she needs a new supply?

If she starts out with exactly six toys, what is the expected value of the number of houses with toddlers that Marie visits without leaving any toys (because the door was not answered) before she needs a new supply?

1. Maria goes to a shooting range. Based on her previous times at the shooting range, she believes she has a 53% chance of hitting the target. Suppose that as part of a training exercise, she has to take ten shots at a moving target.

1. What characteristics of this scenario indicate that you are working with Bernoulli trials?            (3 points)
2. What is the probability that she hits the 4^th target?    (1 point)
3. What is the probability that the first time she hits a target is not until her fourth shot?   (3 points)

Consider the question: What is the probability that she will hit 5 of the targets? Notice that this question is talking about any 5 of the targets and that there are many scenarios in which this could happen. Thus we should apply the binomial model to answer this question. There are two built-in commands for the binomial model in your graphing calculator, binompdf and binomcdf and they can be found by going to 2^nd DISTR and choose option A or B. Use one of these commands to answer the questions (d) through (h) below.

4. What is the probability that she will hit 5 targets?     (3 points)
5. What is the probability that she will hit at most 6 targets?     (3 points)
6. What is the probability that she will hit at least 4 targets?     (3 points)
7. What is the probability that she will hit between 4 and 7 targets (inclusive)?    (3 points)
8. What is the probability that she will hit at least one target?    (3 points)
9. What is the mean and standard deviation of the number of targets hit?    (4 points)

Make Excel do all calculations, using cell addresses. Don’t type numbers in your formulas.

Report the answers to the questions in your worksheet using the appropriate symbols (µ σ) and notation p(x>=5), p(X<3) etc...

            Use Insert/Symbol to find mu and sigma for mean and std dev.

1. An auditor for Health Maintenance Services of Georgia reports 30 percent of policyholders 55 years or older submit a claim during the year. Twelve policyholders are randomly selected for company records.

a. What type of distribution is this likely to be?

b. What is the expected number (mean) of the distribution?

c. What is the standard deviation of the distribution?

Use the tables in your text to answer the following questions

d. What is the probability that exactly 6 of the 12 policyholders have filed a claim?

e. What is the probability that more than 6 of the 12 policyholders have filed a claim?

f. What is the probability that 6 or fewer of the 12 policyholders have filed a claim?

g. What is the probability that at least 6 of the 12 policyholders have filed a claim?

Use the BINOMDIST function to answer the following questions

h. What is the probability that exactly 8 of the 12 policyholders have filed a claim?

i. What is the probability that more than 8 of the 12 policyholders have filed a claim?

j. What is the probability that 8 or fewer of the 12 policyholders have filed a claim?

k. What is the probability that at least 8 of the 12 policyholders have filed a claim?

Read Questions Please. Its different from the others thats been posted!

Information

Six months before its annual convention, the American Medical Association (AMA) must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $100 per room. The AMA believes the number of doctors attending the convention will be has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of $ 160 per room. Assume that there are 8000 rooms available.

[Round your answers to the nearest integer. Also just enter the number. For example, if your answer is $123,456, then enter 123456 without $ and comma.]

Information

Build a simulation model assuming the number of doctors attending the convention follows the following probability distribution.

Run the simulation model 50,000 times.

Question 4 (2 points)

The average number of doctors attending the convention is

Your Answer:

Question 5 (3 points)

The average number of extra rooms needed if they reserve 4000 rooms now is

Your Answer:

Question 6 (3 points)

If they reserve 4000 rooms now, the average number of extra rooms needed is

Your Answer:

Question 7 (3 points)

If they reserve 3000 rooms now, the expected total cost is

Your Answer:

Question 8 (3 points)

If they reserve 6000 rooms now, the expected total cost is

Your Answer:

Suppose that people arrive at a bus stop in accordance with a Poisson process with rate λ. The bus departs at time t.

1. Suppose everyone arrives will wait until the bus comes, i.e., everyone arrives during [0, t] will get on the bus. What is the probability that the bus departs with n people aboard?

2. Let X be the total amount of waiting time of all those who get on the bus at time t. Find E[X]. (Hint: condition on the number of people on the bus.)

Suppose each person arrives at the bus stop will independently wait some time that has an exponential distribution with rate μ . If no bus arrives, he/she will leave the bus stop.

3. What is the probability that the bus departs with n people aboard? (Hint: Thinning a Poisson process, if a person arrives at the bus stop (arriving time uniformly distributed), calculate the probability that he/she will get on the bus)

4. If at time s (s < t), there are k people waiting at the bus stop. What is the expected number of customers who will get on the bus at time t ? (Note some people may leave the bus stop and some may arrive.)