Answer:
a) 0.0668 = 6.68% probability that a domestic airfare is $550 or more
b) 0.1093 = 10.93% probability than a domestic airfare is $250 or less
c) 0.6313 = 63.13% probability that a domestic airfare is between $300 and $500
d) The cost for the 3% highest domestic airfares are $592 and higher.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
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 problem, we have that:
a. What is the probability that a domestic airfare is $550 or more (to 4 decimals)?
This is 1 subtracted by the pvalue of Z when X = 550. So
has a pvalue of 0.9332
1 - 0.9332 = 0.0668
0.0668 = 6.68% probability that a domestic airfare is $550 or more
b. What is the probability than a domestic airfare is $250 or less (to 4 decimals)?
This is the pvalue of Z when X = 250. So
has a pvalue of 0.1093
0.1093 = 10.93% probability than a domestic airfare is $250 or less
c. What if the probability that a domestic airfare is between $300 and $500 (to 4 decimals)?
This is the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 300. So
X = 500
has a pvalue of 0.8519
X = 300
has a pvalue of 0.2206
0.8519 - 0.2206 = 0.6313
0.6313 = 63.13% probability that a domestic airfare is between $300 and $500
d. What is the cost for the 3% highest domestic airfares?
At least the 97th percentile, so at least X when Z has a pvalue of 0.97. So X when Z = 1.88.
The cost for the 3% highest domestic airfares are $592 and higher.
