The scores on a test for a very large class is normally distributed with mean 64 points and
standard deviation 6 points. The department decides to award A to the highest 5% scores.
What is the minimum score to receive an A for the course? Round your answer (down)
to nearest whole number.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.05) to get a Z score. Insert the values in the above equation and solve for the score.
To find the minimum score to receive an A for the course, we need to find the score that corresponds to the top 5% of the distribution. Here's how you can calculate it:
Step 1: Convert the top 5% to a z-score.
In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, the top 5% corresponds to a z-score of approximately 1.645. We can use this value to find the z-score for the score we're looking for.
Step 2: Convert the z-score to an actual score.
Using the formula for z-scores: z = (x - μ) / σ, where z is the z-score, x is the actual score, μ is the mean, and σ is the standard deviation, we can rearrange the equation to solve for x.
x = z * σ + μ
Plugging in the values, we get:
x = 1.645 * 6 + 64
Calculating this, we get:
x ≈ 74.87
Rounding it down to the nearest whole number, the minimum score to receive an A for the course is 74.
Therefore, the answer is 74.