Question

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 not disrupt operations. How often will this even happen, based on this historical information?

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

(a) P(x > 1,814,000) = enter the probability that the daily circulation would pass 1,814,000 (b) P(x < 1,622,000) = enter the probability that the daily circulation will drop below 1,622,000

Answer 1

Solution:

Let X be a random variable which represents the daily circulation of Wall Street journal.

Given that, X ~ N(2276207, 70940²)

i.e.  μ = 2276207 and σ = 70940

a) We have to obtain P(X > 1814000).

We know that if X ~ N(μ ,σ^{​​​​​​2}) then

Using "pnorm" function of R we get, P(Z > -6.52) = 1.0000

1.0000 = 100.00%

Hence, 100.00% of the days circulation would pass 1814000.

b) We have to obtain P(X < 1622000).

We know that if X ~ N(μ ,σ^{​​​​​​2}) then

Using "pnorm" function of R we get, P(Z < -9.22) = 0.0000

0.0000 = 0.00%

Hence, circulation would never drop below 1622000.