Every day, Luann walks to the bus stop and the amount of time she will have to wait for the bus is between 0 and 12 minutes, with all times being equally likely (i. e., a uniform distribution). This means that the mean wait time is 6 minutes, with a variance of 12 minutes. What is the 25th percentile of her total wait time over the course of 60 days? a. 341.902.
b. 349.661.
c. 363.372.
d. 378,099.

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 and standard deviation , the z-score of a measure X is given by:

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 and the standard deviation is

60 days, for each day, mean 6, variance of 12.

So

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.

Thus, the correct answer is given by option A.

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