Question

In: Statistics and Probability

In a recent year, the average daily circulation of the Wall Street Journal was 2,276,207. Suppose...

In a recent year, the average daily circulation of the Wall Street Journal was 2,276,207. Suppose the standard deviation is 70,940. Assume the paper’s daily circulation is normally distributed.

(a) On what percentage of days would circulation pass 1,794,000?

(b) Suppose the paper cannot support the fixed expenses of a full-production setup if the circulation drops below 1,619,000. If the probability of this even occurring is low, the production manager might try to keep the full crew in place and not disrupt operations. How often will this even happen, based on this historical information?

Solutions

Expert Solution

The average daily production of the wall street journal was 2,276,207.

The standard deviation is 70,940.

The paper's daily distribution is normally distributed.

Let, X be the random variable denoting the daily production of papers.

So, X follows the normal distribution with mean 2,276,207 and standard deviation 70,940.

(a) On what percentage of days would circulation pass 1,794,000?

P(X>1,794,000)

=P(X-2,276,207>1,794,000)

=P(X-2,276,207>-482207)

=P(Z>-482207/70940)

Where, Z follows standard normal distribution.

=P(Z>-6.79)

Now, as we know the chance of a standard normal variate lying between -3 and 3 is close to 1, so we can safely say that the chance of the above event is 1.

So, the circulation would pass 1,794,000 on 100% of days, approximately.

(b) Suppose the paper cannot support the fixed expenses of a full-production setup if the circulation drops below 1,619,000. If the probability of this even occurring is low, the production manager might try to keep the full crew in place and not disrupt operations. How often will this even happen, based on this historical information?

ie. to find P(X<1619000)

=P(Z<(1619000-2276207)/70940)

=P(Z<-9.26)

Where, Z is the standard normal variate.

Now, based on the same argument that more than 99% of the standard normal population lies between -3 and 3, so we can say this probability is 0.

So, based on historical info, this will happen approximately 0% of times.


Related Solutions

In a recent year, the average daily circulation of the Wall Street Journal was 2,276,207. Suppose...
In a recent year, the average daily circulation of the Wall Street Journal was 2,276,207. Suppose the standard deviation is 70,940. Assume the paper’s daily circulation is normally distributed. (a) On what percentage of days would circulation pass 1,814,000? (b) Suppose the paper cannot support the fixed expenses of a full-production setup if the circulation drops below 1,622,000. If the probability of this even occurring is low, the production manager might try to keep the full crew in place and...
"A recent articles in the wall street journal reported that the 30-year mortgage rate is now...
"A recent articles in the wall street journal reported that the 30-year mortgage rate is now less than 6 percent. A sample of eight small banks in the Midwest revealed the following 30-year rates (in percent): 4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6 At the 0.01 significance level, can we conclude that the 30-year mortgage rate for small banks is less than 6 percent? (s=0.6346)
Find a story about a recent primary offering in The Wall Street Journal. Based on the...
Find a story about a recent primary offering in The Wall Street Journal. Based on the information in the story, indicate the characteristics of the security sold and the major underwriters. How much new capital did the firm derive from the offering?
Find the most recent summary of the survey of economic forecasters in the Wall Street Journal....
Find the most recent summary of the survey of economic forecasters in the Wall Street Journal. What are the predictions for changes in real GDP and its major components, inflation, and unemployment? Describe the degree of consensus among the various forecasters.
Find the most recent summary of the survey of economic forecasters in the Wall Street Journal...
Find the most recent summary of the survey of economic forecasters in the Wall Street Journal (April 2020). What are the predictions for changes in real GDP and its major components, inflation, and unemployment? Describe the degree of consensus among the various forecasters.
In a recent Wall Street Journal article (“The Price You Pay for Water at the Airport,”...
In a recent Wall Street Journal article (“The Price You Pay for Water at the Airport,” Scott McCartney, April 22, 2015), the cost of a bottle at various airports was compared to the cost of that same bottle of water at a convenience store. A 20-ounce bottle of Dasani water typically costs about $0.99 at a convenience store. At the JFK International airport in New York City, that bottle of Dasani water is $2.89. An airport store operator interviewed for...
QUESTION 1 The Wall Street Journal reported that the average amount of time that a French...
QUESTION 1 The Wall Street Journal reported that the average amount of time that a French person spends eating lunch at a restaurant is 22 minutes. Perform a hypothesis test to determine if a difference exists between the average time an American spends eating lunch when compared to a person from France. The following data represents the time, in minutes, that random French and American diners spent at lunch. Assume that the population variances are unequal. American 21 17 17...
Obtain several recent issues of The Wall Street Journal or Bloomberg Businessweek. Identify, read, and be...
Obtain several recent issues of The Wall Street Journal or Bloomberg Businessweek. Identify, read, and be discuss at least one article relating to one of the six principles of finance. Cite the date and name of the article.
The investing activities of THE WALL STREET JOURNAL INTERACTIVE EDITION subscribers show that the average annual...
The investing activities of THE WALL STREET JOURNAL INTERACTIVE EDITION subscribers show that the average annual number of stock transactions is approximately 15. Suppose a certain investor transacts this frequently. In addition, suppose that the probability of a transaction, for this investor, is the same for any two months, and that the transactions in one month are independent of those that it makes in any other month. a. What is the average number of transactions per month? b. What is...
A recent edition of The Wall Street Journal reported interest rates of 6.2 percent, 6.55 percent,...
A recent edition of The Wall Street Journal reported interest rates of 6.2 percent, 6.55 percent, 6.85 percent, and 6.95 percent for three-year, four-year, five-year, and six-year Treasury notes, respectively. According to the unbiased expectations theory, what are the expected one-year rates for years 4, 5, and 6 (i.e., what are 4f1, 5f1, and 6f1)? (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))       Expected One-Year          Forward Rates     Year 4 %         Year 5 %         Year...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT