The mean cost of domestic airfares in the United States rose to an all-time high of $385 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $110.

a. What is the probability that a domestic airfare is $550 or more (to 4 decimals)?

b. What is the probability than a domestic airfare is $250 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $300 and $500 (to 4 decimals)?

d. What is the cost for the 3% highest domestic airfares?

0.0668

0.1093
0.6325

To answer these questions, we will use the standard normal distribution table or a calculator with a normal distribution function. Here are the steps to find the probabilities and costs:

a. Probability of a domestic airfare being $550 or more:
1. Standardize the value using the formula:
z = (x - mean) / standard deviation
Here, x = $550, mean = $385, and standard deviation = $110.
z = (550 - 385) / 110 = 1.5
2. Lookup the z-value in the standard normal distribution table or use a calculator to find the probability.
P(z > 1.5) = 1 - P(z < 1.5)
The probability is 0.0668 (rounded to 4 decimals).

b. Probability of a domestic airfare being $250 or less:
1. Standardize the value:
z = (x - mean) / standard deviation
Here, x = $250, mean = $385, and standard deviation = $110.
z = (250 - 385) / 110 = -1.2273
2. Lookup the z-value in the standard normal distribution table or use a calculator for the probability.
P(z < -1.2273) = 0.1093 (rounded to 4 decimals).

c. Probability of a domestic airfare being between $300 and $500:
1. Standardize the values for $300 and $500:
z1 = (300 - 385) / 110 = -0.7727
z2 = (500 - 385) / 110 = 1.0455
2. Find the probability of being between these two values using the standard normal distribution table or a calculator.
P(-0.7727 < z < 1.0455) = P(z < 1.0455) - P(z < -0.7727)
The probability is 0.5866 (rounded to 4 decimals).

d. Cost for the 3% highest domestic airfares:
1. Find the z-value corresponding to the 97th percentile (100% - 3% = 97%) using the standard normal distribution table or a calculator.
The z-value is approximately 1.8808.
2. Convert the z-value to the corresponding cost:
cost = (z * standard deviation) + mean
Here, z = 1.8808, standard deviation = $110, and mean = $385.
cost = (1.8808 * 110) + 385 = $595.88 (rounded to the nearest cent).

So, the answers to the questions are:

a. The probability that a domestic airfare is $550 or more is approximately 0.0668.
b. The probability that a domestic airfare is $250 or less is approximately 0.1093.
c. The probability that a domestic airfare is between $300 and $500 is approximately 0.5866.
d. The cost for the 3% highest domestic airfares is approximately $595.88.

0.4332

what if the all-time high price was $385 a ticket?

a. .4332

435