Answer:
[tex]Z = 0.36[/tex]
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem:
I suppose there was a miscue in typing the names, either Emily is Jessica, or we have to find the z-score for Emily's exam.
We have that [tex]\mu = 68, \sigma = 5.5[/tex] and a score of 66, so [tex]X = 66[/tex]
Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{66 - 68}{5.5}[/tex]
[tex]Z = 0.36[/tex]
