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 1,802,000?
(b) Suppose the paper cannot support the fixed
expenses of a full-production setup if the circulation drops below
1,624,000. 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?
Answer:
Given,
mean = 2276207
standard deviation = 70940
a)
To give P(x > 1802000)
= P((x-mu)/s > (1802000 - 2276207)/70940)
= P(z > -6.68)
= 0.9999 [since from z table]
= 1
b)
Now ,
P(x < 1626000)
= P((x-mu)/s < (1624000 - 2276207)/70940)
= P(z < -9.19)
= 0[since from z table]
= 0
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