A population of scores forms a normal distribution with a mean of µ = 40 and a standard deviation of SD = 12. a. What is the probability of randomly selecting a score less than X = 34?
To find the probability of randomly selecting a score less than X = 34 from a normal distribution with a mean of µ = 40 and a standard deviation of SD = 12, we can use the standard normal distribution.
1. Calculate the z-score for X = 34:
The z-score formula is given by:
z = (X - µ) / SD
Substituting the given values:
z = (34 - 40) / 12
z = -6 / 12
z = -0.5
2. Look up the corresponding area under the standard normal distribution curve for the calculated z-score.
You can use a standard normal distribution table or a calculator to find the area. For a z-score of -0.5, the area is approximately 0.3085. This means that approximately 30.85% of the scores are less than X = 34.
Therefore, the probability of randomly selecting a score less than X = 34 is approximately 0.3085 or 30.85%.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to t hat Z score.