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.)
You will find this most useful for these type of questions
http://davidmlane.com/normal.html
enter 78 and 4 for the mean and sd
click on below and enter 80
you should get .6915
so appr the 69 percentile
To find the percentile at which Chris's grade falls, we need to determine the area under the normal curve to the left of his score.
First, we calculate the z-score for Chris's grade using the formula:
z = (x - μ) / σ
where:
x = Chris's score = 80
μ = mean score = 78
σ = standard deviation = 4
Substituting the values:
z = (80 - 78) / 4 = 2 / 4 = 0.5
Next, we need to find the area to the left of z = 0.5. We can use a standard normal distribution table or a calculator. Using a standard normal distribution table, we can find that the area to the left of z = 0.5 is approximately 0.6915.
To convert this to a percentile, we multiply by 100:
percentile = 0.6915 * 100 = 69.15
Rounding to the nearest whole number, Chris's grade falls at approximately the 69th percentile.