Answer:
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To determine the percentage of participants between 3.75 and 5.0 seconds, we can use the concept of the standard normal distribution.
First, we need to standardize the values using the z-score formula:
z = (x - μ) / σ
Where:
- x is the value we want to calculate the percentage for (either 3.75 or 5.0 seconds)
- μ is the mean (average) satisfaction rating, which is 5.5 seconds
- σ is the standard deviation, which is 0.5 seconds
For 3.75 seconds:
z1 = (3.75 - 5.5) / 0.5 = -3.5
For 5.0 seconds:
z2 = (5.0 - 5.5) / 0.5 = -1.0
Next, we can use a standard normal distribution table or a calculator to find the corresponding percentage for each z-score.
From the standard normal distribution table, we find that:
- The percentage of participants with a z-score of -3.5 or lower is approximately 0.0002 (or 0.02%).
- The percentage of participants with a z-score of -1.0 or lower is approximately 0.1587 (or 15.87%).
To find the percentage between 3.75 and 5.0 seconds, we subtract the percentage corresponding to the z-score of 3.75 seconds from the percentage corresponding to the z-score of 5.0 seconds:
Percentage = 0.1587 - 0.0002 = 0.1585 (or 15.85%)
Therefore, approximately 15.85% of the participants will have satisfaction ratings between 3.75 and 5.0 seconds.
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