Shannon is traveling from New York City to Washington, D.C. She wants to go by train so she can see the views. Since she will be driving home with a family member, she only priced the cost of a one-way ticket on Amtrak for any time of day on February 15. Below is an ordered listing of all fares that were available for selection on that day.

$49, 88, 88, 88, 119, 133, 133, 133, 161, 171, 173, 173, 173, 272, 284$

$49, 88, 88, 88, 119, 133, 133, 161, 161, 173, 173, 173, 173, 272, 284$

$88, 88, 88, 119, 119, 133, 133, 161, 161, 173, 173, 173, 272, 272, 284$

$88, 88, 88, 119, 133, 133, 133, 161, 171, 173, 173, 173, 272, 272, 284$

$88, 88, 88, 119, 133, 33, 133$

$88, 88, 88, 119, 133, 133, 133$

$161, 171, 173, 173, 173, 272, 284, 284$

$161$

$171, 173, 173, 173, 272, 284, 284$

a. Find the percentile rank for a fare of $119.

b. Find the percentile rank for a fare of $272.

c. Based on your first two answers, which train fare would have a percentile rank of approximately 82%?

The percentile rank for a fare of $119 is approximately 14%, while the percentile rank for a fare of $272 is approximately 91%. A fare with a percentile rank of approximately 82% would be between $173 and $272.

Explanation:

To find the percentile rank of a given score, we use the formula:

Percentile Rank = (Number of values below the score + 0.5) / Total number of scores × 100

For the fare of $119, count all fares less than $119. There are 7 fares of $88 and 1 fare of $49, giving us 8 fares in total. Using the percentile rank formula:
Percentile Rank for $119 = (8 + 0.5) / 60 × 100 = 14.17%, so approximately the 14th percentile.
For the fare of $272, count all fares less than $272. There are 54 fares less than $272. Using the percentile rank formula:
Percentile Rank for $272 = (54 + 0.5) / 60 × 100 = 90.83%, so approximately the 91st percentile.
To find the fare with a percentile rank of approximately 82%, we need to find the fare where approximately 82% of the other fares are below it. Given the distribution of data, a fare between $173 and $272 would have a percentile rank around 82%.