IF YOU COULD PLEASE CREATE AN EXCEL SPREADSHEET AND ANSWER EACH QUESTION AS A DIFFERENT SHEET. THIS IS AN EXCEL BASED COURSE I NEED TO KNOW HOW TO DO THIS USING EXCEL

Problem 1

Consider the experiment of tossing a coin twice.

a. List the experimental outcomes.

b. Define a random variable that represents the number of heads occurring on the two tosses.

c. Show what value the random variable would assume for each of the experimental outcomes.

d. Is this random variable discrete or continuous?

Problem 2

Nationally, 38% of fourth-graders cannot read an age-appropriate book. The following data show the number of children, by age, identified as learning disabled under special education. Most of these children have reading problems that should be identified and corrected before third grade. Current federal law prohibits most children from receiving extra help from special education programs until they fall behind byapproximately two years' worth of learning, and that typically means third grade or later(USA Today, September 6, 2001).

Age	Number of Children
6	37,369
7	87,436
8	160,840
9	239,719
10	286,719
11	306,533
12	310,787
13	302,604
14	289,168

Suppose that we want to select a sample of children identified as learning disabled under special education for a program designed to improve reading ability. Letxbe a random variable indicating the age of one randomly selected child.

a. Using the data to develop a probability distribution forx. Specify the values for the random variable and the corresponding values for the probability functionf(x).

b. Draw a graph of the probability distribution.

c. Show that the probability distribution satisfies equations Equation 5.1 which isf(x) 0 and Equation 5.2 which is f(x)= 1.

Problem 3

The number of students taking the Scholastic Aptitude Test (SAT) has risen to an all-time high of more than 1.5 million (College Board, August 26, 2008). Students are allowed to repeat the test in hopes of improving the score that is sent to college and university admission offices. The number of times the SAT was taken and the number of students are as follows.

Number of Times	Number of students
1	721,769
2	601,325
3	166,736
4	22,299
5	6730

a. Letxbe a random variable indicating the number of times a student takes the SAT. Show the probability distribution for this random variable.

b. What is the probability that a student takes the SAT more than one time?

c. What is the probability that a student takes the SAT three or more times?

d. What is the expected value of the number of times the SAT is taken? What is your interpretation of the expected value?

e. What is the variance and standard deviation for the number of times the SAT is taken?

Problem 4

The New York City Housing and Vacancy Survey showed a total of 59,324 rent-controlled housing units and 236,263 rent-stabilized units built in 1947 or later. For these rental units, the probability distributions for the number of persons living in the unit are given (U.S. Census Bureau website, January 12, 2004).

Number of Persons	Rent-Controlled	Rent-Stabilized
1	.61	.41
2	.27	.30
3	.07	.14
4	.04	.11
5	.01	.03
6	.00	.01

a. What is the expected value of the number of persons

b. What is the variance of the number of persons living in each type of unit?

c. Make some comparisons between the number of persons living in rent-controlled units and the number of persons living in rent-stabilized units.