The bottom 30% of students failed an end of semester examination. The mean for the test was 120 and the standard deviation was 17. What was the passing score?
you can play around with Z table stuff at
http://davidmlane.com/hyperstat/z_table.html
To find the passing score, we need to determine the cutoff point for the bottom 30% of students.
Step 1: Calculate the z-score for the 30th percentile.
The z-score represents how many standard deviations a particular value is from the mean. We can use a standard normal distribution table or a calculator to find the z-score corresponding to the 30th percentile. In this case, since we are looking for the bottom 30%, we want to find the z-score for the 0.30 percentile.
Step 2: Use the z-score to find the corresponding raw score.
Once we have the z-score for the 30th percentile, we can use the formula z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation. Rearranging the formula, we can solve for X:
X = μ + (z * σ)
Step 3: Calculate the passing score.
Substitute the values for μ (mean) as 120, σ (standard deviation) as 17, and z as the value obtained from step 1 into the equation from step 2 to find the passing score.
Therefore, the passing score can be found by calculating X = 120 + (z * 17), where z is the z-score corresponding to the 30th percentile.