The reaction time of subjects to a certain psychological experiment is considered to be normally distributed with a mean of 20 seconds and a standard deviation of 4 seconds. What is the reaction time such that only 10% of subjects are faster?
To find the reaction time such that only 10% of subjects are faster, we need to find the value of the random variable that corresponds to the 10th percentile of the normal distribution.
Here's how you can calculate it using the standard normal distribution:
1. Start by finding the z-score corresponding to the 10th percentile. This will give us the number of standard deviations below the mean that corresponds to the desired percentile.
To find the z-score, we can use a standard normal distribution table or a statistical software. The z-score corresponding to the 10th percentile is approximately -1.28.
2. Once you have the z-score, you can use it to find the corresponding value in the original distribution by using the formula:
X = µ + (z * σ)
Where:
- X is the desired reaction time
- µ is the mean of the distribution (20 seconds)
- z is the z-score (-1.28)
- σ is the standard deviation of the distribution (4 seconds)
Plugging in the values:
X = 20 + (-1.28 * 4)
X = 20 - 5.12
X ≈ 14.88
Therefore, the reaction time such that only 10% of subjects are faster is approximately 14.88 seconds.