Respuesta :
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:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] 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 [tex]\mu = 56n[/tex], 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 [tex]n = \frac{1}{4}[/tex]. So
[tex]\mu = 56n = \frac{56}{4} = 14[/tex]
The variance is also 14, which means that the standard deviation is [tex]\sqrt{14} = 3.74[/tex]
The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.
