The durations of phone calls taken by the receptionist at an office are like draws made at random with replacement from a list that has an average of 8.5 minutes (that's 8 minutes and 30 seconds) and an SD of 3 minutes. Approximately what is the chance that the total duration of the next 100 calls is more than 15 hours?

Question

kropot72 · Answer

$$X=\frac{15\times 60}{100}=9\ minutes$$
$$z=\frac{X-\mu}{\sigma}=\frac{9-8.5}{3}=0.1667$$
Reference to a standard normal distribution table shows that the cumulative probability of calls averaging less than 9 minutes is 0.5662. Therefore the chance that the total duration of the next 100 calls is more than 15 hours is 1.0000 - 0.5662

anonymous · Answer

@kropot72 that's incorrect , thnx