Respuesta :
Answer:
a. 341.902.
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.
n instances of a normal variable:
For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]
60 days, for each day, mean 6, variance of 12.
So
[tex]\mu = 60*6 = 360[/tex]
[tex]s = \sqrt{12}\sqrt{60} = 26.8328[/tex]
What is the 25th percentile of her total wait time over the course of 60 days?
X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-0.675 = \frac{X - 360}{26.8328}[/tex]
[tex]X - 360 = -0.675*26.8328[/tex]
[tex]X = 341.902[/tex]
Thus, the correct answer is given by option A.
