Question:
Problem 6.65: In According to Editor and Publisher Yearbook, the average daily circulation of The Wall Street Journal based on 1994 figures is 1,818,562. The standard deviation is 50,940.

A. Assume the paper's daily circulation is normally distributed. On what percentage of days would it surpass a circulation of 1,850,000?

B. Suppose the paper cannot support the fixed expenses of a full-production setup if the circulation drops below 1,700,000. If the probability of this event occuring is low, the production manager might try to keep the full crew in place and not disrupt operations. How often will this event happen, based on the historical information?

A.:
Assume the paper's daily circulation is normally distributed. On what percentage of days would it surpass a circulation of 1,850,000?

Solution / Formula:

z = (x - m ) / s

(1,850,000 - 1,818,562) / 50,940

z = 0.6172
(using the z table) = 0.2324

.5000 - .2324 = .2676

Answer:

P (X>1,850,000) = 0.2676 or 26.76%

Suppose the paper cannot support the fixed expenses of a full-production setup if the circulation drops below 1,700,000. If the probability of this event occuring is low, the production manager might try to keep the full crew in place and not disrupt operations. How often will this event happen, based on the historical information?

Solution / Formula:

z = (x - m ) / s

(1,700,000 - 1,818,562) / 50,940

z = -2.3275
(using the z table) = 0.4901

.5000 - .4901 = .0099

Answer:

P (X<1,700,000) = 0.0099 or .99%

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