Answer:
(a) The first quartile is 382.27 and it means that at least el 25% of the scores are less than 382.27 points.
The second quartile is 462 and it means that at least el 50% of the scores are less than 462 points.
The third quartile is 541.73 and it means that at least el 75% of the scores are less than 541.73 points.
(b) The 99th percentile is 739.27 and it means that at least el 99% of the scores are less than 739.27 points.
Step-by-step explanation:
The first, second the third quartile are the values that let a probability of 0.25, 0.5 and 0.75 on the left tail respectively.
So, to find the first quartile, we need to find the z-score for which:
P(Z<z) = 0.25
using the normal table, z is equal to: -0.67
So, the value x equal to the first quartile is:
Then, the first quartile is 382.27 and it means that at least el 25% of the scores are less than 382.27 points.
At the same way, the z-score for the second quartile is 0, so:
So, the second quartile is 462 and it means that at least el 50% of the scores are less than 462 points.
Finally, the z-score for the third quartile is 0.67, so:
So, the third quartile is 541.73 and it means that at least el 75% of the scores are less than 541.73 points.
Additionally, the z-score for the 99th percentile is the z-score for which:
P(Z<z) = 0.99
z = 2.33
So, the 99th percentile is calculated as:
So, the 99th percentile is 739.27 and it means that at least el 99% of the scores are less than 739.27 points.
