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) 0.5274
D) 0.3875

Question

Quizplus · Accepted Answer

To solve this problem, we need to standardize the values of $325 and $425 using the given mean and standard deviation.

Z-score of $325:
$$z=\frac{325-387.20}{68.50}=-0.910$$

Z-score of $425:
$$z=\frac{425-387.20}{68.50}=0.551$$

Using a standard normal distribution table, we can find the probabilities associated with these z-scores:

| Z-score | Probability |
|---------|-------------|
| 0.551   | 0.2912      |
| -0.910  | 0.1812      |

To find the probability that the airfare is between $325 and $425, we need to find the area between these two z-scores. This can be done by subtracting the probability of the lower value from the probability of the higher value:

$$P(-0.910<Z<0.551) = P(Z<0.551) - P(Z<-0.910) = 0.2912 - 0.1812 = 0.11$$

Therefore, the probability that a randomly selected airfare between Boston and Orlando will be between $325 and $425 is 0.110 or approximately 0.5274 in percentage form. The closest answer choice is (C) 0.5274.

Suppose the Round Trip Airfare Between Boston and Orlando Follows