Suppose the round-trip airfare between Boston and Orlando 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 Boston and San Francisco will be between $325 and $425?
A) 0.2650
B) 0.1548
C) 0.5275
D) 0.3875

Question

Quizplus · Accepted Answer

To solve this problem, we need to standardize the values of $325 and $425 using the formula:
$Z = \frac{X - \mu}{\sigma}$, where $X$ is the value we want to standardize, $\mu$ is the mean and $\sigma$ is the standard deviation.

For $X = 325$:
$Z = \frac{325 - 387.20}{68.50} \approx -0.9108$

For $X = 425$:
$Z = \frac{425 - 387.20}{68.50} \approx 0.5504$

We need to find the probability that a randomly selected airfare will fall between $325 and $425, which is equivalent to finding the area under the normal curve between the standardized values of $-0.9108$ and $0.5504$. Using a standard normal table or calculator, we find that this probability is approximately 0.5275. Therefore, the answer is C.

Suppose the Round-Trip Airfare Between Boston and Orlando Follows the Normal