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?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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)
|
|
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4
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New York Daily News (NY)
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|
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5
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Chicago Tribune (IL)
|
|
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6
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Washington Post (DC)
|
|
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7
|
Las Vegas Review-Journal (NV)
|
|
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8
|
Minneapolis Star Tribune (MN)
|
|
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9
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Denver Post (CO)
|
|
|
10
|
St. Petersburg Tampa Bay Times (FL)
|
|
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11
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Philadelphia Inquirer (PA)
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|
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12
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Boston Globe (MA)
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13
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Dallas Morning News (TX)
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14
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Houston Chronicle (TX)
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15
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Austin American-Statesman (TX)
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|
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16
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Newark Star-Ledger (NJ)
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17
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Phoenix Republic (AZ)
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|
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18
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Springfield Republican (MA)
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19
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San Francisco Chronicle (CA)
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20
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Chicago Sun-Times (IL)
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21
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San Diego Union-Tribune (CA)
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|
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22
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Seattle Times (WA)
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|
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23
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Kansas City Star (MO)
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|
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24
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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
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