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

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Quizplus · Accepted Answer

To find the probability that a randomly selected airfare is between $325 and $425, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For $325: $Z = \frac{325 - 387.20}{68.50} = -0.9078$. For $425: $Z = \frac{425 - 387.20}{68.50} = 0.5515$. Looking these Z-scores up in the standard normal distribution table gives the probabilities of 0.1823 and 0.7097, respectively. The probability of being between these two values is the difference: 0.7097 - 0.1823 = 0.5274.

Suppose the Round-Trip Airfare Between Philadelphia and Los Angeles a Month