MGMT2262 Tutorial Sheet #4

The print time for a photocopier to copy 20 pages is uniformly distributed between 20.2 and 21.6 seconds.

1) What is the probability the print time for 20 pages is less than 21 seconds? (57.14%)

2) What is the probability the print time for 20 pages is more than 20.5 seconds? (78.57%)

3) Confirm Chebyshev’s theorem for k=2. (see key)

Suppose a company has 5 customer service reps (CSR) in its call centre at any given time. They collectively serve 40 customers per hour on average.

4) What is the probability a customer waits more than 2 minutes to speak to a CSR? (26.36%)

5) What is the probability a customer waits more than 2 minutes if they’ve been waiting 30 seconds already? (36.79%)

6) Suppose there are only 4 CSR instead of 5. What is the probability a customer waits more than 2 minutes? (34.42%)

7) If there are only 4 CSR, what is the probability a customer will speak to a CSR within 2 minutes if they’ve been waiting 30 seconds already? (55.07%)

Sales at a particular store are normally distributed with a mean of $30 and a standard deviation of $12.50.

8) What is the probability that a single sale is less than $35? (0.6554)

9) What is the probability that a single sale is more than $50? (0.0548)

10) What is the probability that a single sale is between $25 and $50? (0.6006)

11) What is the cutoff point for an individual sale to place in the top 10% of sales? Round to the nearest cent. ($46.03)

12) What is the cutoff point for an individual sale to place in the bottom 2% of sales? Round to the nearest cent. ($4.31)