An instructor in a large lecture class found at the end of the semester that total points scored by students in his class was approximately Normal with mean 530 and standard deviation 80. If 10% of the class are to receive A's (he grades on a curve), what is the lowest number of points for a student to earn an A?
A. 632
B. 610
C. 428
Here is how to find the answer:
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 (.10) and its Z score and insert the values into the above equation to find the Raw score.
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To find the lowest number of points for a student to earn an A, we need to determine the cutoff point that corresponds to the top 10% of scores.
Since the distribution of total points scored by students is approximately normal with a mean of 530 and a standard deviation of 80, we can use the Z-score formula to find the cutoff point.
The Z-score formula is given by:
Z = (X - μ) / σ
Where:
Z = Z-score
X = Raw score
μ = Mean
σ = Standard deviation
To find the cutoff point for the top 10% of scores, we need to find the Z-score that corresponds to the 90th percentile.
Using a Z-table or a calculator, we can find that the Z-score corresponding to the 90th percentile is approximately 1.28.
Now, we can rearrange the Z-score formula to solve for the raw score (X):
X = Z * σ + μ
Plugging in the values:
X = 1.28 * 80 + 530
X ≈ 610
Therefore, the lowest number of points for a student to earn an A is approximately 610.
So, the correct answer is B. 610.