A environmental monitoring group collected 200 soil samples from a nature reserve and reco… — GRE General Test

A environmental monitoring group collected $200$ soil samples from a nature reserve and recorded their pH levels in the frequency table below:

What percent of the soil samples with a pH level of at least $6.0$ have a pH level in the range $6.0$ to $7.9$ ?

75.00\%

To find the desired percentage, first restrict the sample space to all soil samples having a pH level of at least

6.0

. Adding the frequencies for

6.0–6.9

(

70

7.0–7.9

(

50

8.0–8.9

(

30

), and

9.0–9.9

(

10

) gives a base total of

160

samples. Next, find the number of samples within that group that fall in the range

6.0

7.9

, which is

70 + 50 = 120

. The percentage is calculated as

(120 / 160) \times 100\% = 75.00\%

Determine the conditional base population (samples with pH

\ge 6.0

Sum of frequencies for ranges

6.0-6.9

7.0-7.9

8.0-8.9

, and

9.0-9.9

70 + 50 + 30 + 10 = 160

The question asks 'of the soil samples with a pH level of at least 6.0', which restricts the total base to these four intervals.

Determine the target frequency (samples with pH in range

6.0

7.9

Sum of frequencies for ranges

6.0-6.9

and

7.0-7.9

70 + 50 = 120

This captures all qualifying samples within the specified target interval.

Calculate the conditional percentage.

\frac{120}{160} \times 100\% = 0.75 \times 100\% = 75.00\%

Divide the target sub-group count by the conditional base count and convert to a percentage.

Conditional Relative Frequency in Grouped Data Tables

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