The probability that an srs of 100 freshmen has a mean unweighted gpa between 3.75 and 3.95 is 21.77%
Finding the probability of a mean unweighted gpa between 3.75 and 3.95.
From the question, we have the following parameters that can be used in our computation:
Mean = 3.81
Standard deviation = 0.36
Scores = 3.75 and 3.95
The z-score of these values can be calculated using
z = (Score - Mean)/SD
So, we have
z = (3.75 - 3.81)/0.36 and z = (3.95 - 3.81)/0.36
z = -0.167 and z = 0.389
So, the probability is represented as
P = (-0.167 < z < 0.389)
Using the z table of probabilities, we have
P = 0.2177
This gives
P = 21.77%
Hence, the probability is 21.77%
Question
The incoming freshman class at north carolina state university had a mean unweighted gpa of 3.81 with a standard deviation of 0.36. these gpas are normally distributed.
Find the probability that an srs of 100 freshmen has a mean unweighted gpa between 3.75 and 3.95.