Answer each question: 2.146) Five cards are drawn from a standard 52-card playing deck. What is the probability that all 5 cards will be of the same suit? 2.162) Assume that there are nine parking...

Answer each question:
2.146)
Five cards are drawn from a standard 52-card playing deck. What is the probability that all 5 cards will be of the same suit?
2.162)
Assume that there are nine parking spaces next to one another in a parking lot. Nine cards need to be parked by an attendant. Three of the cars are expensive sports cars, three are large domestic cars, and three are imported compacts. Assuming that the attendant parks the cars at random, what is the probability that the three expensive sports cars are parked adjacent to one another?
3.180)
Four possibly winning numbers for a lottery-AB-4536, NH-7812, SQ-7855, and ZY-3221- arrive in the mail. You will win a prize if one of your numbers matches one of the winning numbers contained on a list held by those conducting the lottery. One first prize of $100,000m two second prizes of $50,000 each, and ten third prizes of $1000 each will be awarded. To be eligible to win, you need to mail the coupon back to the company at a cost of 33 cents for postage. No purchase is required. From the structure of the numbers that you received it is obvious the numbers sent out consist of two letters followed by four digits. Assuming that the numbers you received were generated at random, what are your expected winnings from the lottery? Is it worth 33 cents to enter this lottery?
3.14)
The maximum patent life for a new drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life for the drug that is, the length of time that the company has to recover research and development costs and to make profit. The distribution of the lengths of actual patent lives for new drugs is given below:
Years, y 3 4 5 6 7 8 9 10 11 12 13
p(y) .03 .05 .07 .10 .14 .20 .18 .12 .07 .03 .01

1. Find the mean patent life for a new drug.


2. Find the standard deviation of Y= the length of life of a ramdom selected new drug.


3. What is the probability that the value of Y falls in the interval µ+ 2s?

3.108)
A shipment of 20 cameras include 3 that are defective> What is the minimum number of cameras that must be selected if we require that P(at least 1 defective) = 0.8?
4.160)
Let the density function of a random variable Y be given by
f(x) =

1. Find the distribution function


2. Find E(Y)

4.62)
If Z is a standard normal random variable, what is

1. P(Z²
   


2. P(Z²
   

4.88)
The magnitude of earthquakes recorded in a region of North America can be modeled as having an exponential distribution with mean 2.4, as measured on the Richer scale. Find the probability that an earthquake striking this region will

1. Exceed 3.0 on the Richter scale


2. Fall between 2.0 and 3.0 on the Richter scale

4.124)
The percentage of impurities per batch in a chemical product is a random variable Y with density function
f(y) =

A batch with more that 40% impurities cannot be sold.

1. Integrate the density directly to determine the probability that a randomly selected batch cannot be sold because of excessive impurities.\


2. Use applet Beta Probabilities and Quantiles to find the answer to part (a).

4.136)
Suppose that the waiting time for the first customer to enter a retail shop after 9:00 a.m. is a random variable Y with an exponential density function given by
f(y)=

1. Find the moment generating function for Y.


2. Use the answer from part (a) to find E(Y) and V(Y)

4.144)
Consider a random variable Y with density function given by
f(y) = k, -

1. Find k


2. Find the moment generating function of Y


3. Find E(Y) and V(Y)

4.146)
A manufacture of tires wants to advertise a mileage interval that excludes no more than 10% of the mileage on tires he sells. All he knows is that, for a large number of tires tested, the mean mileage was 25,000 miles, and the standard deviation was 4000 miles. What interval would you suggest?