Suppose that the scores of a history test are normally distributed with a mean of 565 and a standard deviation of 113. a) What percentage of the scores are less than 450?

15.39% of the scores are less than 450

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 percentage of the scores are less than 450?

This is the pvalue of Z when X = 450. So

has a pvalue of 0.1539

15.39% of the scores are less than 450

step-by-step explanation:

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