Telcom a telephone answering service for businesses has foun

Telcom, a telephone answering service for businesses has found that the average telephone message is 150 seconds, with a standard deviation of 15 sees. It has also found that the length of messages is normally distributed. Using your Normal Tables, determine the probability that a single message will last more than 180 secs

Solution

The mean of the telephone message is 150 seconds and the standard deviation is 15 seconds.

For a normal distribution, 95% of the values are within 2 standard deviations of the mean. Therefore, 95% of the values lie between 120 and 180. This implies, 10% of the values lie above 180 and below 120.

Since the normal curve is symmetric about the mean implies that 5% of the values lie above 180.

Hence, the probability that the message is more than 180 seconds is \"0.05\"