Question

In: Statistics and Probability

A) Phone calls arrive at a particular call center with an average of 12 every minute....

A) Phone calls arrive at a particular call center with an average of 12 every minute. The call center management want the maximum probability of having more calls than staff in any given minute being .2. How many staff are necessary to ensure this?

Use Excel to help you find the answer.

B) Consider the 1981 Super Bowl commercial from Schlitz involving a live taste test. Schlitz sponsored a live taste test for its beer during the half time of the 1981 Super Bowl. Suppose that a taste tester preferring Schlitz is considered a success which occurs with probability .4. In a sample of 80 what is the probability that 40 or more will choose Schlitz as the best beer?

Solutions

Expert Solution

a) The number of calls per minute here is modelled as:

We first compute the CDF for X here for the first few values as:
P(X <= 0) = P(X = 0)
P(X <= 1) = P(X = 0) + P(X = 1)
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) and so on....

This is computed in EXCEL as:

x P(X <= x) Formula
0 6.14421E-06 =POISSON.DIST(AH5,12,TRUE)
1 7.98748E-05 =POISSON.DIST(AH6,12,TRUE)
2 0.000522258 =POISSON.DIST(AH7,12,TRUE)
3 0.002291791 =POISSON.DIST(AH8,12,TRUE)
4 0.007600391 =POISSON.DIST(AH9,12,TRUE)
5 0.020341029 =POISSON.DIST(AH10,12,TRUE)
6 0.045822307 =POISSON.DIST(AH11,12,TRUE)
7 0.089504497 =POISSON.DIST(AH12,12,TRUE)
8 0.155027782 =POISSON.DIST(AH13,12,TRUE)
9 0.242392162 =POISSON.DIST(AH14,12,TRUE)
10 0.347229418 =POISSON.DIST(AH15,12,TRUE)
11 0.461597333 =POISSON.DIST(AH16,12,TRUE)
12 0.575965249 =POISSON.DIST(AH17,12,TRUE)
13 0.681535632 =POISSON.DIST(AH18,12,TRUE)
14 0.772024532 =POISSON.DIST(AH19,12,TRUE)
15 0.844415652 =POISSON.DIST(AH20,12,TRUE)
16 0.898708993 =POISSON.DIST(AH21,12,TRUE)
17 0.937033703 =POISSON.DIST(AH22,12,TRUE)

We see from the above table that:
P(X <= 14) = 0.7720
P(X <= 15) = 0.8444

As we want here that maximum probability of having more calls than staff in any given minute being .2, therefore the staff required here is given as 14. Therefore 14 is the staff size required here.

b) We are given the number of successes here modelled as:

Probability that 40 or more will choose Schlitz as the best beer is computed using the EXCEL function for binomial probability function here as:

P(X >= 40) = 1 - P(X <= 39)

This is computed in EXCEL as:
=1-binom.dist(39,80,0.4,TRUE)

0.0445 is the output here.
Therefore 0.0445 is the required probability here.

orchestra answered 1 year ago
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