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Answer:
Bella's score on the exam is 87.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
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, we have that:
Arturo's score on the exam is 75
His score is Z standard deviations above the mean
Bella’s score is 1.5 standard deviations above Arturo’s score.
So Bella's z-score is 1.5 + 0.625 = 2.125.
Her score is the value of X when Z = 2.125. So:
Bella's score on the exam is 87.