Call Center. A customer calling a call center spends an average of 16 minutes on

Question

Call Center. A customer calling a call center spends an average of 16 minutes on hold during the peak season, with a standard deviation of 4 minutes. Suppose these times are gamma distributed with shape parameter a and scale parameter b determined form the information supplied. Find the probability that the customer will be on hold (a) more than 22 minutes, (b) between 10 and 20 minutes. (c) Find x* such that 5% of the callers will be on hold for more than x* minutes. Hint: Be careful, b is scale parameter. What are mean and variance of gamma r,v. in terms of shape and scale?

Explanation / Answer

given mean =16

std =4

a) We want

P(X >22)= z =( 22 -16)/4=6/4=1.5   FROM STANDARD Z TABLE WE HAVE VALUE

P(X>22)=1-0.9332=0.0668

b) between 10 and 20

p(x<10<20) =

z1=(10-16)/4 =-6/4=-1.5 from standard z table we have value is 0.0668

z2=(20-16)/4) = 1 = 0.8413 from standard z table we have value

p(x<10<20) == 0.8413-0.0668 0.7745

c) x* such that 5% of the callers will be on hold for moe than x* mmin

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