1.

A football team consists of 18 freshmen and 18 sophomores, 15 juniors, and 12 seniors.

Four players are selected at random to serve as captains. Find the probability that at least 1 of the students is a senior.

2.

If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of

three, he wins $20. The cost to play the game is $5. What is the expectation of this game?

3.

Determine the indicated probability for a binomial experiment with the given number of

trials n and the given success probability p.

n=13, p=0.7, P(Fewer than 4)

4.

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is

estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 18 adult dogs is studied. What is the standard deviation of the number of dogs who weigh 65 lb or more?

5.

If there are 20 typographical errors randomly distributed in a 250-page document, find

the probability that a given page contains exactly two errors.

6.

Last year, a manufacturer produced 1,850,000 DVD players. Of these, approximately 2%

were defective. Assume that a simple random sample of n=220 players is drawn. Use the Poisson approximation to the binomial distribution to compute the probability that exactly fourteen of the 220 DVD players were defective.

7.

The average charitable contribution itemized per income tax return in Pennsylvania is

$792. Suppose that the distribution of contributions is normal with a standard deviation of $103. Find the limits for the middle 50% of contributions

8.

X is a normally distributed random variable with a standard deviation of 3.00. Find the

mean of Xif 12.71% of the area under the distribution curve lies to the right of 11.42. (Note: the diagram is not necessarily to scale.)

ment

9.

A sample of size 36 will be drawn from a population with mean 27 and standard

deviation 13. Find the probability that x will be greater than 30.

10.

A ferry will safely accommodate 70 tons of passenger cars. Assume that the mean weight 17)

of a passenger car is 1.7 tons with standard deviation 0.7 tons. If a random sample of 37 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded?

11.

A ferry will safely accommodate 82 tons of passenger cars. Assume that the mean weight

of a passenger car is 1.9 tons with standard deviation 0.6 tons. If a random sample of 40 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded?

12.

Use the normal approximation to find the indicated probability. The sample size is n, the

population proportion of successes is p, and X is the number of successes in the sample.

n=90, p=0.53: P(X<50)

13.

A biologist estimates that 40% of the deer in a region carry a certain type of tick. For a

sample of 300 deer selected at random, what is the chance that 124 or fewer deer have this tick?

For each of the following uncertain quantities, discuss whether it is reasonable to assume that the probability distribution of the quantity is binomial. If you think it is, what are the parameters n and p? If you think it isn’t, explain your reasoning.

a. The number of wins the Boston Red Sox baseball team has next year in its 81 home games

b. The number of free throws Kobe Bryant misses in his next 250 attempts

c. The number of free throws it takes Kobe Bryant to achieve 100 successes

d. The number out of 1000 randomly selected customers in a supermarket who have a bill of at least $150

e. The number of trading days in a typical year where Microsoft’s stock price increases

f. The number of spades you get in a 13-card hand from a well-shuffled 52-card deck

g. The number of adjacent 15-minute segments during a typical Friday where at least 10 customers enter a McDonald’s restaurant

h. The number of pages in a 500-page book with at least one misprint on the page.

A dentist's chair with a person in it weighs 1875 N. The output plunger of a hydraulic system starts to lift the chair when the dental assistant's foot exerts a force of 36 N on the input piston. Neglecting any difference in the heights of the piston and the plunger, what is the ratio of the area of the plunger to the area of the piston?

Aplunger

Apiston

=

An elevator accelerates upward at 1 m/s2. When the elevator is moving upward at 2 m/s, a bolt drops from the ceiling which is 2.5 m above the ?oor. Assume that the bolt does not experience air resistance. Calculate how long it takes for the bolt to hit the ?oor, how far it travels, and how fast it is going when it hits the ?oor of the elevator. Solve this problem in two reference frames, one ?xed with respect to the building and one ?xed with respect to the elevator. Only the fall time will be the same for the two reference frames. In this and subsequent problems you solve in dynamics, think about the advantages and disadvantages of various reference frames and clearly state what reference frame you ultimately choose for your solution.

For all the baseball fans out there: Assuming that two teams are evenly matched in the World Series (a championship series of at most 7 games; the first team to win 4 games wins the Series) so that the probability of each team winning each game is 50%, and assuming each game is independent of each other game, what is the probability that the Series will be won in exactly 4 games? 5? 6? that the Series goes to game 7?

Lee and Martin compete in an arcade game where the two have to press a button as soon as an alarm sound is triggered. Who presses the button first wins. Suppose the response times of Lee and Martin, X1 and X2, are independent random variables where Xi is exponentially distributed with rate λi.
a) What is the distribution of the time between the alarm sound and the first response?

b) What is the probability that the time until the first response exceeds T?

c) Suppose the game is played for n rounds and the response times of Lee and Martin are independent and identically distributed across different games. What is the variance of the number of rounds in which the response time exceeds T?

A student implemented scenario A simulation. However, testing intra-VLANS using ping commands did not work. Why a ping might fail? (choose all answers which apply)

Incomplete ports configurations as tranks

Bandwidth limitations on Trunks

Missed VLAN ID in the list of allowed VLANS on a trunk link

Using apple computers instead of Microsoft as hosts

Incorrect Ip assighment for hosts in same VLANs

Not using the latest host operating system update

A piston in a gasoline engine is in simple harmonic motion. The engine is running at the rate of 3 410 rev/min. Taking the extremes of its position relative to its center point as ±4.50 cm.

(a) Find the magnitude of the maximum velocity of the piston.
m/s

(b) Find the magnitude of the maximum acceleration of the piston
km/s²

From the information below I need to find the best predicted probability of having a new client give the highest level of satisfaction.

The first item you want to highlight is your customer satisfaction record. Over the past 18 months of employment you have worked with 24 clients, and according to the customer satisfaction surveys all clients are asked to take after their contract is completed, 22 of them rated you with the highest level of satisfaction. Use this information to find the best predicted probability of having a new client give the highest level of satisfaction.

An elevator with mass 500 Kg starts from rest and moves upward 20.0 m in 5.00 s. What is the average rate with which the force from the cable is doing work on the elevator?
g = 9.8 m / s2