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zubka84 [21]
2 years ago
10

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, wit

h 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.
Mathematics
1 answer:
Nana76 [90]2 years ago
3 0

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

Z = \frac{X - \mu}{\sigma}

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 n\mu and the standard deviation is s = \sigma\sqrt{n}

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

So

\mu = 60*6 = 360

s = \sqrt{12}\sqrt{60} = 26.8328

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.

Z = \frac{X - \mu}{s}

-0.675 = \frac{X - 360}{26.8328}

X - 360 = -0.675*26.8328

X = 341.902

Thus, the correct answer is given by option A.

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