The class average on the quarterly exam was65% with a standard deviation of 7%. Is the probability that a student got 70% or higher 24%

Here is your stats calculator.

http://davidmlane.com/normal.html

enter 65 for mean
enter 7 for SD
click on "above" and enter 70

you should see .2375

So what do you think?

To determine the probability that a student got 70% or higher on the quarterly exam, we need to use the concept of standard scores (also known as z-scores). A standard score measures how many standard deviations a particular score is from the mean.

First, find the z-score for a score of 70% using the formula:
z = (x - μ) / σ

Where:
z = z-score
x = score we want to find the probability for (70% in this case)
μ = mean (class average) = 65%
σ = standard deviation = 7%

Plugging in the values:
z = (70 - 65) / 7

Calculating:
z = 5 / 7 ≈ 0.714

Next, we need to find the probability associated with this z-score using a standard normal distribution table or calculator. This table gives us the area under the standard normal curve from the left-hand side.

Looking up the z-score of 0.714 in the table, we find that the corresponding probability is approximately 0.7611.

Therefore, the probability that a student scored 70% or higher on the quarterly exam is approximately 0.7611 or 76.11%, not 24%.