Respuesta :
Answer:
X = 101.48
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.
Average of 62 seconds with a standard deviation of 24.5 seconds.
This means that [tex]\mu = 62, \sigma = 24.5[/tex]
If the manager wants to advertize that 95% of the time, they serve customers within X seconds, what is the value of X?
This is the 95th percentile of times, which is X when Z has a p-value of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 62}{24.5}[/tex]
[tex]X - 62 = 1.645*24[/tex]
[tex]X = 101.48[/tex]
