Questions: On each trial of an experiment, a subject is presented with a constant soft noise, which is interrupted at some unpredictable time by a noticeably louder sound. The time it takes for the subject to react to this louder sound is recorded. The following list contains the reaction times (in milliseconds) for the 16 trials of this experiment: 296, 171, 271, 250, 217, 241, 311, 164, 152, 193, 231, 235, 236, 257, 273, 285 Send data to calculator Find 25th and 60th percentiles for these reaction times. (If necessary, consult a list of formulas.) (a) The 25th percentile: milliseconds (b) The 60th percentile: milliseconds

On each trial of an experiment, a subject is presented with a constant soft noise, which is interrupted at some unpredictable time by a noticeably louder sound. The time it takes for the subject to react to this louder sound is recorded. The following list contains the reaction times (in milliseconds) for the 16 trials of this experiment: 296, 171, 271, 250, 217, 241, 311, 164, 152, 193, 231, 235, 236, 257, 273, 285 Send data to calculator Find 25th and 60th percentiles for these reaction times. (If necessary, consult a list of formulas.) (a) The 25th percentile: milliseconds (b) The 60th percentile: milliseconds
Transcript text: On each trial of an experiment, a subject is presented with a constant soft noise, which is interrupted at some unpredictable time by a noticeably louder sound. The time it takes for the subject to react to this louder sound is recorded. The following list contains the reaction times (in milliseconds) for the 16 trials of this experiment: \[ 296,171,271,250,217,241,311,164,152,193,231,235,236,257,273,285 \] Send data to calculator Find $25^{\text {th }}$ and $60^{\text {th }}$ percentiles for these reaction times. (If necessary, consult a list of formulas.) (a) The $25^{\text {th }}$ percentile: $\square$ milliseconds (b) The $60^{\text {th }}$ percentile: $\square$ milliseconds
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Solution

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Solution Steps

Step 1: Sort the Data

The data points are sorted in ascending order: [152, 164, 171, 193, 217, 231, 235, 236, 241, 250, 257, 271, 273, 285, 296, 311].

Step 2: Calculate the Index (I)

The index \(I\) is calculated using the formula \(I = \frac{25}{100} \times (16 + 1) = 4.25\).

Step 3: Determine the Percentile Value

Since \(I\) is not a whole number, we interpolate between the two nearest data points to find the percentile value, which is 199.

Final Answer:

The 25th percentile of the given data set is 199.

Step 1: Sort the Data

The data points are sorted in ascending order: [152, 164, 171, 193, 217, 231, 235, 236, 241, 250, 257, 271, 273, 285, 296, 311].

Step 2: Calculate the Index (I)

The index \(I\) is calculated using the formula \(I = \frac{60}{100} \times (16 + 1) = 10.2\).

Step 3: Determine the Percentile Value

Since \(I\) is not a whole number, we interpolate between the two nearest data points to find the percentile value, which is 251.

Final Answer:

The 60th percentile of the given data set is 251.

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