26. General Hospital\'s patient account division has compiled data on the age of

Question

26. General Hospital's patient account division has compiled data on the age of accounts recievable. The data collected indicate that the age of accounts follows a normal distribution with µ = 28 and a = 8 days.

A. What portion of the accounts is between 20 and 40 days old - that is, P(20 x 40)

B. The hospital administrator is interested in sending reminder letters to the oldest 15% of accounts. How many days old should an account be before a reminder letter is sent?

C. The hosipital administrator wants to give a discount to those accounts that pay their balance by the twenty-first day. What percentage of the accounts will receive the discount?

Explanation / Answer

a) P(20<X<40)=P((20-28)/8<Z<(40-28)/8)=P(-1<Z<1.5)=0.9332-0.1587 =0.7745

b) for highest 15%, z=1.0364

hence number of days =28+1.0364*8=36.29 days

c) P(X<21) =P(Z<(21-28)/8)=P(Z<-0.875)=0.1908~19.08%

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