Professor Halen teaches a College Mathematics class. The scores on the midterm exam are normally distributed with a mean of 72.3 and a standard deviation of 8.9. What is the probability that a student scores between 82 and 90

14.63% probability that a student scores between 82 and 90

Step-by-step explanation:

Problems of normally distributed samples are 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:

What is the probability that a student scores between 82 and 90?

This is the pvalue of Z when X = 90 subtracted by the pvalue of Z when X = 82. So

X = 90

has a pvalue of 0.9649

X = 82

has a pvalue of 0.8186

0.9649 - 0.8186 = 0.1463

14.63% probability that a student scores between 82 and 90

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step-by-step explanation: