Question

travel is the only thing you buy that makes you richer.
anonymous

1. what do you think this person meant in this quote? (2 points)

handwritten text: \traveling is expensive and you will spend a lot of money\

most cities have some form of taxicab services for short - distance trips. usually the cab fares are either a flat fee for a specified distance or a metered fee. the metered cabs often start with an initial fee and then charge a fixed rate per fraction of a mile driven. in many cities, wait time and number of stops often affect the fare as well. the website taxifarefinder.com offers a ranking of cities by the cost of a hypothetical taxi trip of a given duration and distance. of the top 80 most expensive cities, these are the initial cab fees in ranked order:

1.95, 2.70, 2.85, 3.00, 3.00, 3.00, 3.00, 3.10, 3.50, 3.50
2.10, 2.80, 2.85, 3.00, 3.00, 3.00, 3.00, 3.25, 3.50, 4.00
2.30, 2.85, 2.85, 3.00, 3.00, 3.00, 3.00, 3.50, 3.50, 4.00
2.50, 2.85, 2.85, 3.00, 3.00, 3.00, 3.00, 3.50, 3.50, 4.00
2.50, 2.85, 2.85, 3.00, 3.00, 3.00, 3.00, 3.50, 3.50, 4.00
2.50, 2.85, 2.85, 3.00, 3.00, 3.00, 3.00, 3.50, 3.50, 4.95
2.60, 2.85, 2.85, 3.00, 3.00, 3.00, 3.00, 3.50, 3.50, 5.75
2.60, 2.85, 2.85, 3.00, 3.00, 3.00, 3.00, 3.50, 3.50, 10.00

a. determine the percentile rank for an initial fee of $2.85.

Explanation:

Step1: Count total data points

There are 8 rows and 10 columns, so total \( n = 8\times10 = 80 \) data points.

Step2: Count values less than 2.85

Values less than 2.85: 1.95, 2.10, 2.30, 2.50, 2.50, 2.50, 2.60, 2.60. That's 8 values.

Step3: Count values equal to 2.85

Let's count: In each row, how many 2.85?
Row 1: 1 (2.85)
Row 2: 2 (2.80? No, 2.85: 2.85, 2.85? Wait, row 2: 2.10, 2.80, 2.85, 3.00,... So 2.85: 1? Wait no, let's list all 2.85:
Row 1: 2.85 (1)
Row 2: 2.85 (1)
Row 3: 2.85, 2.85 (2)
Row 4: 2.85, 2.85 (2)
Row 5: 2.85, 2.85 (2)
Row 6: 2.85, 2.85 (2)
Row 7: 2.85, 2.85 (2)
Row 8: 2.85, 2.85 (2)
Wait, let's recount:
Row 1: [1.95, 2.70, 2.85, 3.00, 3.00, 3.00, 3.00, 3.10, 3.50, 3.50] → 1 (2.85)
Row 2: [2.10, 2.80, 2.85, 3.00, 3.00, 3.00, 3.00, 3.25, 3.50, 4.00] → 1 (2.85)
Row 3: [2.30, 2.85, 2.85, 3.00, 3.00, 3.00, 3.00, 3.50, 3.50, 4.00] → 2 (2.85)
Row 4: [2.50, 2.85, 2.85, 3.00, 3.00, 3.00, 3.00, 3.50, 3.50, 4.00] → 2 (2.85)
Row 5: [2.50, 2.85, 2.85, 3.00, 3.00, 3.00, 3.00, 3.50, 3.50, 4.00] → 2 (2.85)
Row 6: [2.50, 2.85, 2.85, 3.00, 3.00, 3.00, 3.00, 3.50, 3.50, 4.95] → 2 (2.85)
Row 7: [2.60, 2.85, 2.85, 3.00, 3.00, 3.00, 3.00, 3.50, 3.50, 5.75] → 2 (2.85)
Row 8: [2.60, 2.85, 2.85, 3.00, 3.00, 3.00, 3.00, 3.50, 3.50, 10.00] → 2 (2.85)
Total equal to 2.85: \( 1 + 1 + 2 + 2 + 2 + 2 + 2 + 2 = 14 \)

Step4: Apply percentile formula

Percentile rank \( = \frac{\text{Number of values less than } x + 0.5\times\text{Number of values equal to } x}{n} \times 100 \)
So \( \frac{8 + 0.5\times14}{80} \times 100 = \frac{8 + 7}{80} \times 100 = \frac{15}{80} \times 100 = 18.75 \)

Answer:

18.75