Answer:
[tex]z= \frac{69 -65.2}{11.68}=0.325[/tex]
And we can find the probability:
[tex] P(Z<0.325) = 0.627[/tex]
And that correcpond to the 63 percentile approximated.
Step-by-step explanation:
We have the following dataset:
45, 62, 63, 58, 81, 77, 64, 69, 82, 51.
In order to find this problem we need to assume a distribution for the data. If we assume that the scores are normally distributed we can use the z score in order to find the percentile for the 69 value.
First we need to find the mean and deviation with the following formulas:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}=65.2[/tex]
[tex]\sigma=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n}}=11.68[/tex]
And then we can find the z score with the following formula:
[tex] z= \frac{X -\mu}{\sigma}[/tex]
If we replace for X =69 we got this:
[tex]z= \frac{69 -65.2}{11.68}=0.325[/tex]
And we can find the probability:
[tex] P(Z<0.325) = 0.627[/tex]
And that correcpond to the 63 percentile approximated.
