The bottom 30% of the students failed an end of semester exam. The mean for the test was 130 and the standard deviation was 27. What was the passing score?
36
To find the passing score, we need to determine the score below which 30% of the students fall.
First, let's calculate the z-score for the bottom 30% of the students. The z-score represents the number of standard deviations a data point is from the mean. We can use a standard normal distribution table or a calculator to find the z-score.
To find the z-score corresponding to 30% of the area under the normal curve, we need to find the z-score that has an area of 0.30 to the left.
Looking at the standard normal distribution table, we find that a z-score of -0.52 has an area of 0.3015 to the left.
Next, we can use the z-score formula to find the passing score:
z-score = (Score - Mean) / Standard Deviation
Plugging in the values, we have:
-0.52 = (Score - 130) / 27
Now we can solve for the passing score:
-0.52 * 27 = Score - 130
-14.04 = Score - 130
Score = -14.04 + 130
Score = 115.96
Therefore, the passing score is approximately 116.
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 (.30) and its Z score. Insert data into above equation to solve for the score.