Answer to Question #169735 in Statistics and Probability for Miu

Question

According to the Audit Bureau of Circulations, the top 25 city newspapers in the United States ranked according to circulation are:

Rank

Newspaper

1 New York Times (NY)

2 Los Angeles Times (CA)

3 New York Post (NY)

4 New York Daily News (NY)

5 Chicago Tribune (IL)

6 Washington Post (DC)

7 Las Vegas Review-Journal (NV)

8 Minneapolis Star Tribune (MN)

9 Denver Post (CO)

10 St. Petersburg Tampa Bay Times (FL)

11 Philadelphia Inquirer (PA)

12 Boston Globe (MA)

13 Dallas Morning News (TX)

14 Houston Chronicle (TX)

15 Austin American-Statesman (TX)

16 Newark Star-Ledger (NJ)

17 Phoenix Republic (AZ)

18 Springfield Republican (MA)

19 San Francisco Chronicle (CA)

20 Chicago Sun-Times (IL)

21 San Diego Union-Tribune (CA)

22 Seattle Times (WA)

23 Kansas City Star (MO)

24 Pittsburgh Post-Gazette (PA)

25 Sacramento Bee (CA)

Suppose a researcher wants to sample a portion of these newspapers and compare the sizes of the business sections of the Sunday papers. She randomly samples eight of these newspapers.

a. What is the probability that the sample contains exactly one newspaper located in New York state?

b. What is the probability that half of the sampled newspapers are ranked in the top 10 by circulation?

c. What is the probability that none of the newspapers is located in California?

d. What is the probability that exactly three of the newspapers are located in states that begin with the letter M?

(Round your answers to 4 decimal places.)

a. P(x = 1 in NY) = 

enter probability rounded to 4 decimal places

b. P(x = 4 in top 10) = 

enter probability rounded to 4 decimal places

c. P(x = 0 in California) = 

enter probability rounded to 4 decimal places

d. P(x = 3 with M) = 

enter probability rounded to 4 decimal places

Answer 1

a.  Proabability of newsapaper originated in new york p =$\dfrac{4}{25}$

$q=1-p=1-\dfrac{4}{25}=\dfrac{21}{25}$

$P(x = 1 \text{ in } NY)$ = $^{8}C_1(\dfrac{4}{25})^1(\dfrac{21}{25})^{7}$

= $8\times 0.16\times 0.295=0.3777$

b. Probability of top 10 newspaper p =$\dfrac{10}{25}=\dfrac{2}{3}$

$q=1-p=1-\dfrac{2}{3}=\dfrac{1}{3}$

 P(x = 4 in top 10) = $^{10}C_4(\dfrac{2}{3})^4(\dfrac{1}{3})^6$

=$210\times 0.1975\times0.00137=0.0569$

c.  Probability of newspaper located in california $p=\dfrac{4}{25}$

$q=1-p=1-\dfrac{4}{25}=\dfrac{21}{25}$

P(x = 0 in California) = $^8C_0(\dfrac{4}{25})^0(\dfrac{21}{25})^8$

=$1\times 1\times0.247875=0.2479$

d.  Probability of newspaper from state whose name start with letter m $p=\dfrac{4}{25}$

$q=1-p=1-\dfrac{4}{25}=\dfrac{21}{25}$

P(x = 3 with M) = $^8C_3(\dfrac{4}{25})^3(\dfrac{21}{25})^5$

= $56\times 0.004096\times 0.41821=0.0959$