One hundred students took a statistics exam where the mean score was 78. The distribution was normal. The standard deviation was 4. If Chris earned an 80 on the exam, at approximately what percentile did his grade fall? (Round your answer to the nearest whole number.)
Mean=78
SD=4
x=80
80-78/4=0.5
Look in the back of your statistics textbook for a table called something like “area under normal distribution” to find the proportion/probability in larger portion of Z = .5. Multiply by 100.
To find the approximate percentile at which Chris' grade falls, you can use the standard normal distribution table. Here's how you can do it:
1. Standardize the score by calculating the z-score. The formula for calculating the z-score is:
z = (x - μ) / σ
where x is Chris' score (80 in this case), μ is the mean (78), and σ is the standard deviation (4).
So, plugging in the values:
z = (80 - 78) / 4
z = 2 / 4
z = 0.5
2. Look up the z-score in the standard normal distribution table. The z-score of 0.5 corresponds to approximately 0.6915.
3. Convert the z-score to a percentile by multiplying it by 100:
percentile = 0.6915 * 100
percentile ≈ 69
Therefore, Chris' grade of 80 falls at approximately the 69th percentile.