Answer:
89.44%
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
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 question:
[tex]\mu = 45, \sigma = 5.6[/tex]
If you score 52 on the test, what percentage of test takers scored lower than you?
This is the pvalue of Z when X = 52.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{52 - 45}{5.6}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.8944.
So 89.44% of test takers scored lower than you.
