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 related to the Z score. Multiply by 15.
To find the number of students who scored above 85%, we need to use the concept of standard deviation and the normal distribution.
Here's how we can calculate it:
Step 1: Find the z-score of 85%.
The z-score tells us how many standard deviations a particular value is from the mean in a normal distribution. To find the z-score, we can use the formula:
z = (x - μ) / σ
where:
- x is the value we want to find the z-score for (85%),
- μ is the mean (74.8%),
- σ is the standard deviation (7.57).
So, for 85%, the z-score is:
z = (85 - 74.8) / 7.57
Step 2: Use the z-table to find the proportion of scores above the z-score.
The z-table provides the proportion of scores that lie below a given z-score. To find the proportion above the z-score, we subtract the table value from 1. The z-table value can be found using statistical software or by looking it up in a standard normal distribution table.
Step 3: Convert the proportion to the number of students.
Multiply the proportion above the z-score by the total number of students to find the number of students who scored above 85%.
That's how you can find the number of students who scored above 85% in this problem.