Suppose scores on a college entrance exam are normally distributed with a mean of 550 and a standard deviation of 100. Find the probability that a student taking the test will score less than 400. Round to four decimal places.

0.0668 = 6.68% probability that a student taking the test will score less than 400.

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:

Find the probability that a student taking the test will score less than 400.

This is the pvalue of Z when X = 400. So

has a pvalue of 0.0668

0.0668 = 6.68% probability that a student taking the test will score less than 400.

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step-by-step explanation: