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Answer :
To find the percentile corresponding to a given radiation level of [tex]\(1.44 \, \frac{W}{kg}\)[/tex], you can follow these steps:
1. List the Radiation Levels: First, note down all the given radiation levels in order. We have a total of 50 radiation levels.
2. Identify the Target Level: We are focusing on the radiation level of [tex]\(1.44 \, \frac{W}{kg}\)[/tex] and need to determine its position relative to the rest of the levels.
3. Count Lower Levels: Count how many of the radiation levels are less than [tex]\(1.44 \, \frac{W}{kg}\)[/tex]. In this case, there are 45 levels that are less than [tex]\(1.44 \, \frac{W}{kg}\)[/tex].
4. Calculate the Percentile: The percentile is calculated using the formula:
[tex]\[
\text{Percentile} = \left( \frac{\text{Number of levels less than the target}}{\text{Total number of levels}} \right) \times 100
\][/tex]
Substituting the numbers we have:
[tex]\[
\text{Percentile} = \left( \frac{45}{50} \right) \times 100 = 90
\][/tex]
5. Round the Percentile: In this case, the percentile is already a whole number, so no further rounding is needed.
Therefore, the radiation level of [tex]\(1.44 \, \frac{W}{kg}\)[/tex] corresponds to the 90th percentile.
1. List the Radiation Levels: First, note down all the given radiation levels in order. We have a total of 50 radiation levels.
2. Identify the Target Level: We are focusing on the radiation level of [tex]\(1.44 \, \frac{W}{kg}\)[/tex] and need to determine its position relative to the rest of the levels.
3. Count Lower Levels: Count how many of the radiation levels are less than [tex]\(1.44 \, \frac{W}{kg}\)[/tex]. In this case, there are 45 levels that are less than [tex]\(1.44 \, \frac{W}{kg}\)[/tex].
4. Calculate the Percentile: The percentile is calculated using the formula:
[tex]\[
\text{Percentile} = \left( \frac{\text{Number of levels less than the target}}{\text{Total number of levels}} \right) \times 100
\][/tex]
Substituting the numbers we have:
[tex]\[
\text{Percentile} = \left( \frac{45}{50} \right) \times 100 = 90
\][/tex]
5. Round the Percentile: In this case, the percentile is already a whole number, so no further rounding is needed.
Therefore, the radiation level of [tex]\(1.44 \, \frac{W}{kg}\)[/tex] corresponds to the 90th percentile.
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