Suppose that a deck of 52 cards contains 26 red cards and 26 black cards. Say we use the 52 cards to randomly distribute 13 cards each among two players (2 players receive 13 card each).

a. How many ways are there to pass out 13 cards to each of the two players?

b. What is the probability that player 1 will receive 13 cards of one color and player 2 receive 13 cards of the other color?

The Sorry State Lottery requires you to select five different numbers from 0 through 63. (Order is not important.) You are a Big Winner if the five numbers you select agree with those in the drawing, and you are a Small-Fry Winner if four of your five numbers agree with those in the drawing. (Enter your answers as exact answers.)

What is the probability of being a Big Winner?

What is the probability of being a Small-Fry Winner?

What is the probability that you are either a Big Winner or a Small-Fry Winner?

Contracts for two construction jobs are randomly assigned to one or more of three firms A, B, and C. Let Y1 denote the number of contracts assigned to firm A and Y2 the number of contracts assigned to firm B. Recall that each firm can receive 0, 1 or 2 contracts.

(a) Find the joint probability function for Y1 and Y2.

(b) Find the marginal probability of Y1 and Y2.

(c) Are Y1 and Y2 independent? Why?

(d) Find E(Y1 − Y2).

(e) Find Cov(Y1, Y2)

Exercise 5a: What is the recommend number of classes for 1.5, 2.2, 3.4,3.4,3.4 ,4.5, 5.1?

Exercise 5b: What is a good class width?

Exercise 5c: Give the frequency distribution.

Exercise 5d. Make a list of the lower limits of all classes

Exercise 5e: Make two columns in Excel, one with all observations (1.5,2.2,...) and one with the lower limits. Delete the lowest number in the lower limit column. This is your bin column

.Exercise 5f: In the Excel Data Toolpak, choose histogram. Enter the numbers and the bins. Show the chart in your homework

Exercise 5g: Compare with the manual chart

A diagnostic test either provides a + result (has the disease) or - result (does not have the disease). 5% of the population has the disease. For a patient with the disease, 75% will test (+)/ 25% will test (-). For a patient that does not have the disease, 15 % will test (+)/ 85% will test (-).

Part A) If everyone in the population is tested, what proportion of the test results will be positive?

Part B) For a patient who gets a Positive result, what is the probability of having the disease?

A frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. What is the area associated with the class? Select one: a. -2.0 and -1.0 b. 1.0 and 2.0 c. 0.8185 d. 0.4772 e. 0.1359

The following sample data are from a normal population: 10, 9, 12, 14, 13, 11, 7, 4.

a. What is the point estimate of the population mean?

b. What is the point estimate of the population standard deviation (to 2 decimals)?

c. With 95% confidence, what is the margin of error for the estimation of the population mean (to 1 decimal)?

d. What is the 95% confidence interval for the population mean (to 1 decimal)?
( , )

Q: Suppose a new treatment for a certain disease is given to a sample of 200 patients. The treatment was successful for 164 of the patients. Assume that these patients are representative of the population of individuals who have this disease. Calculate a 98% confidence interval for the proportion successfully treated. (Round the answers to three decimal places.)

A: ___ to ___

For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fall independently of each other and that each component has a 0.21 probability of failure.

(A) Would it be unusual to observe one component fail? Two components?
Fill in blanks:
It (would,would not) be unusual to observe one component fail, since the probability that one component fails,___is, (less,greater) than 0.05. It (would not, would) be unusual to observe two components fail, since the probability that two components fail ____, is (greater,less) than 0.05

The following ratings (R) and observed times (OT) represent the elements from question 1. Using the ratings (R) given below for each observation, determine the normal time (NT) for each element. Using the PD&F allowance factor you developed above from question 1, complete the summary and calculate the elemental standard times for each element. Times are in seconds.

A template (which is optional) is available in the course content page, under the Test 3 module.

Q#1

The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5.10 years and a standard deviation of 2.00 years. Random samples of size 12 are drawn from the population and the mean of each sample is determined. Round the answers to the nearest hundredth.

Q#2

A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be less than 12.1 ounces. Find the probability if the sample is just 1 cup.

Here is a census for an apportionment problem in a hypothetical country comprised of four states. • State of Ambivalence: 8,000; • State of Boredom: 9,000; • State of Confusion: 24,000; • State of Depression: 59,000. (100,000 total) Assume that the house has h = 10 seats to apportion to these four states. What apportionment is determined by the method of: Hamilton, Adam, Jefferson, Webster.

Soma recorded in the table the height of each player on the basketball team

Construct a normal probability distribution curve for this population! Indicate the number for the mean, 1SD, 2SD and 3SD (both sides of the mea) (1+ 6*0.5=4p)