A study of first year QPA’s has been taken. The following data have been found: The average first year QPA is 2.4 with an SD of 0.5, and tends to follow a normal curve. About what percentage of QPA’s fall between 2.0 and 2.9?
To find the percentage of QPAs that fall between 2.0 and 2.9, we need to find the area under the normal curve between these two values.
First, we need to standardize the values using the z-score formula:
z = (x - μ) / σ
For 2.0:
z1 = (2.0 - 2.4) / 0.5 = -0.8
For 2.9:
z2 = (2.9 - 2.4) / 0.5 = 1.0
Next, we need to find the area under the normal curve between these two z-scores. We can use a z-table or a calculator to find these values.
The z-table gives us the cumulative probability of z-scores. Looking up the z-scores -0.8 and 1.0 in the table, we find the corresponding cumulative probabilities are 0.2119 and 0.8413, respectively.
To find the percentage between 2.0 and 2.9, we subtract the cumulative probability of 2.0 (0.2119) from the cumulative probability of 2.9 (0.8413):
0.8413 - 0.2119 = 0.6294
So, approximately 62.94% of QPA's fall between 2.0 and 2.9.