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?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.10) related to the Z score. Insert Z score in equation above and solve for the score.
To find the reaction time such that only 10% of subjects are faster, we need to determine the z-score corresponding to a cumulative probability of 0.10.
The formula to find the z-score is: z = (x - μ) / σ
Where:
- z is the z-score
- x is the value we want to find (reaction time)
- μ is the mean of the distribution (20 seconds)
- σ is the standard deviation of the distribution (4 seconds)
To find the z-score corresponding to a cumulative probability of 0.10, we can use a standard normal distribution table or a calculator. The z-score can also be found using the inverse cumulative distribution function (CDF) of the standard normal distribution.
Using a standard normal distribution table, we find that a cumulative probability of 0.10 corresponds to a z-score of -1.28.
Now, we can calculate the reaction time (x) using the z-score formula:
-1.28 = (x - 20) / 4
Simplifying the equation:
-1.28 * 4 = x - 20
-5.12 = x - 20
x = -5.12 + 20
x = 14.88
Therefore, the reaction time such that only 10% of subjects are faster is approximately 14.88 seconds.