The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?
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 15.
To find the number of students who scored above 85%, we need to calculate the z-score for 85% in the normal distribution.
The z-score is a measure of how many standard deviations an individual value is from the mean. We can calculate the z-score using the formula:
z = (X - μ) / σ
where X is the individual value, μ is the mean, and σ is the standard deviation.
In this case, X is 85%, μ is 74.8%, and σ is 7.57.
z = (85 - 74.8) / 7.57
z = 1.34
Next, we need to find the area under the normal curve corresponding to a z-score of 1.34, which represents the percentage of students who scored below 85%. We can use a standard normal distribution table or calculate it using statistical software. Let's assume the area is 0.9099.
Since the total area of the normal distribution is 1, to find the percentage of students who scored above 85%, we can subtract the area below 85% from 1.
Percentage above 85% = 1 - 0.9099
Percentage above 85% = 0.0901
To find the number of students who scored above 85%, we multiply the percentage by the total number of students.
Number of students above 85% = 0.0901 * 15
Number of students above 85% ≈ 1.35
Rounding to a whole number, we can approximate that approximately 1 or 2 students scored above 85%.