Statistics Questions and Analysis

The questions to be answered are;

Data showing the population by state in millions of people follow (The World Almanac, 2012). The dataset in Excel file 2012Population.xlsx.

a. Develop a frequency distribution, a percent frequency distribution, and a histogram. Use a class width of 2.5 million.

b. Does there appear to be any skewness in the distribution? Explain. 

c. What observations can you make about the population of the 50 states?

Forty-three percent of Americans use social media and other websites to voice their opinions about television programs (the Huffington Post, November 23, 2011). Below are the results of a survey of 1364 individuals who were asked if they use social media and other websites to voice their opinions about Television programs

Uses Social Media and Other Websites to Voice Opinions About Television Programs     Doesn’t Use Social Media and Other Websites to Voice Opinions About Television Programs

Female 395                                                                                                               291

Male 323                                                                                                                   355

a. Show a joint probability table.

b. What is the probability a respondent is female?

c. What is the conditional probability a respondent uses social media and other websites to voice opinions about television programs given the respondent is female? 

d. Let F denote the event that the respondent is female and A denote the event that the respondent uses social media and other websites to voice opinions about television programs. Are events F and A independent?

The average starting salary for this year's graduates at a large university (LU) is $20,000 with a standard deviation of $8,000. Furthermore, it is known that the starting salaries are normally distributed.

a. What is the probability that a randomly selected LU graduate will have a starting salary of at least $30,400? 

b. What is the probability that a randomly selected LU graduate will have a salary of exactly $30,400?

c. Individuals with starting salaries of less than $15600 receive a low income tax break. What percentage of the graduates will receive the tax break?

d. If 189 of the recent graduates have salaries of at least $32240, how many students graduated this year from this university? 

The College Board reported the following mean scores for the three parts of the SAT (The World Almanac, 2009):

Critical reading 502

Mathematics 515

Writing 494

Assume that the population standard deviation on each part of the test is 100.

a) What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical reading part of the test? 

b) What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test? Compare this probability to the value computed in part (a).