Question

Difficulty: MediumFrequency Distributions, Tables, and Grouped Data

The table below shows the frequency distribution of daily rainfall, in millimeters, recorded across 50 weather monitoring stations during a storm event.

Daily Rainfall (mm)Number of Stations
0 to under 1010
10 to under 2015
20 to under 3017
30 to under 405
40 to under 503

What percentage of the stations that recorded at least 10 mm of daily rainfall recorded less than 30 mm of daily rainfall?

  1. A
    42.5%42.5\%
  2. B
    64%64\%
  3. C
    75%75\%
  4. 80%80\%Answer
  5. E
    84%84\%

Answer

80%80\%
To find the desired percentage, first identify the total number of stations that recorded at least 10 mm of rainfall. This includes the intervals 10 to under 20, 20 to under 30, 30 to under 40, and 40 to under 50, giving 15+17+5+3=4015 + 17 + 5 + 3 = 40 stations. Next, find how many of these 40 stations recorded less than 30 mm. These fall into the 10 to under 20 and 20 to under 30 intervals, which total 15+17=3215 + 17 = 32 stations. Calculating the relative percentage gives (32/40)×100%=80%(32 / 40) \times 100\% = 80\%.

Step-by-Step Solution

1
Determine the conditional base (denominator)
Sum the frequencies for all intervals representing at least 10 mm: 15+17+5+3=4015 + 17 + 5 + 3 = 40 stations.
The question specifies 'stations that recorded at least 10 mm of daily rainfall', restricting our population base to this subset.
2
Determine the target subgroup frequency (numerator)
Sum the frequencies for intervals within the base that are also less than 30 mm (the 10 to under 20 and 20 to under 30 intervals): 15+17=3215 + 17 = 32 stations.
We need to count the stations that meet both conditions: at least 10 mm and less than 30 mm.
3
Calculate the percentage
3240×100%=0.80×100%=80%\frac{32}{40} \times 100\% = 0.80 \times 100\% = 80\%.
Divide the target subgroup count by the conditional base count and multiply by 100.

Key Concept

Grouped frequency table interpretation with conditional percentages
Estimated Time:1m 30s
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