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 for the Z score. Multiply by 100.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability for the Z score. Multiply by 100.
Step 1: Standardize the pass mark
To standardize the pass mark, we need to calculate the z-score. The z-score formula is given by:
z = (X - μ) / σ
where X is the value we are standardizing (in this case, the pass mark), μ is the mean of the distribution, and σ is the standard deviation.
Substituting the values into the formula:
z = (20 - 25) / 10
z = -0.5
Step 2: Find the proportion of students passing
To find the proportion of students passing, we need to find the area to the right of the z-score (-0.5) in the standard normal distribution table. This area represents the percentage of students scoring above the pass mark.
Using a standard normal distribution table or a statistical calculator, we find that the area to the right of -0.5 is approximately 0.6915.
Step 3: Calculate the number of students passing
To calculate the number of students passing, we need to multiply the proportion found in Step 2 by the total number of students (100).
Number of students passing = 0.6915 * 100
Number of students passing ≈ 69 (rounded to the nearest whole number)
Therefore, we estimate that approximately 69 students passed the examination.