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storchak [24]
3 years ago
9

Suppose the round-trip airfare between Philadelphia and Los Angeles a month before the departure date follows the normal probabi

lity distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between these two cities will be between $325 and $425?
Mathematics
1 answer:
QveST [7]3 years ago
7 0

Answer:

52.74% probability that a randomly selected airfare between these two cities will be between $325 and $425

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 387.20, \sigma = 68.50

What is the probability that a randomly selected airfare between these two cities will be between $325 and $425?

This is the pvalue of Z when X = 425 subtracted by the pvalue of Z when X = 325. So

X = 425

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

Z = \frac{425 - 387.20}{68.50}

Z = 0.55

Z = 0.55 has a pvalue of 0.7088

X = 325

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

Z = \frac{325 - 387.20}{68.50}

Z = -0.91

Z = -0.91 has a pvalue of 0.1814

0.7088 - 0.1814 = 0.5274

52.74% probability that a randomly selected airfare between these two cities will be between $325 and $425

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