Answer:
The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which
x is the number of sucesses
e = 2.71828 is the Euler number
 is the mean in the given interval. The variance is the same as the mean.
 is the mean in the given interval. The variance is the same as the mean.
Average rate of 56 calls per hour:
This means that  , in which n is the number of hours.
, in which n is the number of hours.
Find the average and standard deviation of the number of service calls in a 15-minute period.
15 minute is one fourth of a hour, which means that  . So
. So

The variance is also 14, which means that the standard deviation is 
The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.