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?

Answer 1

Answer:

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 $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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:

$\mu = 60, \sigma = 5$

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

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

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{45 - 60}{5}$

$Z = -3$

$Z = -3$ has a pvalue of 0.0013

0.13% of students have scored less than 45 points