What is the common score amount all 100 gymnasts?
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The approximate value of P(-0.78 ≤ Z ≤ 1.16) is obtained being 0.6593
<h3>How to get the z scores?</h3>If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have
(X is following normal distribution with mean and standard deviation
)
then it can be converted to standard normal distribution as
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
Also, know that if we look for Z = z in z-tables, the p-value we get is
For this case, we have to find:
It can be rewritten as:
The p-values for Z = 1.16 and Z = -0.78 from the z-table is found as 0.8770 and 0.2177 respectively, and therefore, we get:
Thus, the approximate value of P(-0.78 ≤ Z ≤ 1.16) is obtained being 0.6593
Learn more about z-score here: