## The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points.

Question

The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points. About what percent of students have scored less than 45 points?

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2 weeks 2021-09-15T03:22:10+00:00 1 Answer 0

0.13% of students have scored less than 45 points

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:

About what percent of students have scored less than 45 points?

This is the pvalue of Z when X = 45. So

has a pvalue of 0.0013

0.13% of students have scored less than 45 points