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Answer :
Certainly! Let's answer each question step-by-step based on the provided fares.
a. Find the percentile rank for a fare of [tex]$119.
To find the percentile rank of a fare, you use the formula:
\[ \text{Percentile Rank} = \frac{\text{Number of fares less than or equal to the fare}}{\text{Total number of fares}} \times 100 \]
Given fare: $[/tex]119
Step-by-step calculation:
1. Count the number of fares less than or equal to [tex]$119.
2. Divide this count by the total number of fares.
3. Multiply the result by 100 to get the percentile rank.
Let's summarize:
- The total number of fares is 90.
- There are 27 fares that are less than or equal to $[/tex]119.
Using the provided solution:
[tex]\[ \text{Percentile Rank for } \$119 = \frac{27}{90} \times 100 \approx 30.00\% \][/tex]
So, the percentile rank for a fare of [tex]$119 is \( \boxed{30.00\%} \).
b. Find the percentile rank for a fare of $[/tex]272.
Given fare: [tex]$272
Step-by-step calculation:
1. Count the number of fares less than or equal to $[/tex]272.
2. Divide this count by the total number of fares.
3. Multiply the result by 100 to get the percentile rank.
Let's summarize:
- The total number of fares is 90.
- There are 82 fares that are less than or equal to [tex]$272.
Using the provided solution:
\[ \text{Percentile Rank for } \$[/tex]272 = \frac{82}{90} \times 100 \approx 91.11\% \]
So, the percentile rank for a fare of [tex]$272 is \( \boxed{91.11\%} \).
c. Based on your first two answers, which train fare would have a percentile rank of approximately 82%?
To find the fare corresponding to the 82nd percentile:
- We need to look at the sorted list of fares and find the fare that approximately matches the 82nd percentile.
- The fare corresponding to a certain percentile means finding the fare where the cumulative percentage is close to that percentile.
Step-by-step:
1. Look through the sorted list of fares.
2. Identify the fare where the percentile rank first reaches or surpasses 82%.
From the given solution:
- The fare which has a percentile rank close to 82% is $[/tex]173.
So, the train fare with approximately 82% percentile rank is [tex]\( \boxed{\$173} \)[/tex].
Here are the final answers for the questions:
a. Percentile rank for [tex]$119 is \( \boxed{30.00\%} \).
b. Percentile rank for $[/tex]272 is [tex]\( \boxed{91.11\%} \)[/tex].
c. Train fare with approximately 82% percentile is [tex]\( \boxed{\$173} \)[/tex].
a. Find the percentile rank for a fare of [tex]$119.
To find the percentile rank of a fare, you use the formula:
\[ \text{Percentile Rank} = \frac{\text{Number of fares less than or equal to the fare}}{\text{Total number of fares}} \times 100 \]
Given fare: $[/tex]119
Step-by-step calculation:
1. Count the number of fares less than or equal to [tex]$119.
2. Divide this count by the total number of fares.
3. Multiply the result by 100 to get the percentile rank.
Let's summarize:
- The total number of fares is 90.
- There are 27 fares that are less than or equal to $[/tex]119.
Using the provided solution:
[tex]\[ \text{Percentile Rank for } \$119 = \frac{27}{90} \times 100 \approx 30.00\% \][/tex]
So, the percentile rank for a fare of [tex]$119 is \( \boxed{30.00\%} \).
b. Find the percentile rank for a fare of $[/tex]272.
Given fare: [tex]$272
Step-by-step calculation:
1. Count the number of fares less than or equal to $[/tex]272.
2. Divide this count by the total number of fares.
3. Multiply the result by 100 to get the percentile rank.
Let's summarize:
- The total number of fares is 90.
- There are 82 fares that are less than or equal to [tex]$272.
Using the provided solution:
\[ \text{Percentile Rank for } \$[/tex]272 = \frac{82}{90} \times 100 \approx 91.11\% \]
So, the percentile rank for a fare of [tex]$272 is \( \boxed{91.11\%} \).
c. Based on your first two answers, which train fare would have a percentile rank of approximately 82%?
To find the fare corresponding to the 82nd percentile:
- We need to look at the sorted list of fares and find the fare that approximately matches the 82nd percentile.
- The fare corresponding to a certain percentile means finding the fare where the cumulative percentage is close to that percentile.
Step-by-step:
1. Look through the sorted list of fares.
2. Identify the fare where the percentile rank first reaches or surpasses 82%.
From the given solution:
- The fare which has a percentile rank close to 82% is $[/tex]173.
So, the train fare with approximately 82% percentile rank is [tex]\( \boxed{\$173} \)[/tex].
Here are the final answers for the questions:
a. Percentile rank for [tex]$119 is \( \boxed{30.00\%} \).
b. Percentile rank for $[/tex]272 is [tex]\( \boxed{91.11\%} \)[/tex].
c. Train fare with approximately 82% percentile is [tex]\( \boxed{\$173} \)[/tex].
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