Respuesta :
Answer:
0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean 5,500 and standard deviation 1,000.
This means that [tex]\mu = 5500, \sigma = 1000[/tex]
What is the probability that the call center will get between 4,800 and 5,000 calls in a day?
This is the p-value of Z when X = 5000 subtracted by the p-value of Z when X = 4800. So
X = 5000
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5000 - 5500}{1000}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a p-value of 0.3085.
X = 4800
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4800 - 5500}{1000}[/tex]
[tex]Z = -0.7[/tex]
[tex]Z = -0.7[/tex] has a p-value of 0.2420.
0.3085 - 0.2420 = 0.0665
0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.
