Question

The mean score on a final chemistry exam was 75, and the standard deviation of the scores was 5. If the distribution is normal and your score was 70, what percentage of the scores was lower than yours

Answer 1

Answer:

15.87% of the scores was lower than yours

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:

$\mu = 75, \sigma = 5$

If the distribution is normal and your score was 70, what percentage of the scores was lower than yours

This is the pvalue of Z when X = 70. So

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

$Z = \frac{70 - 75}{5}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

15.87% of the scores was lower than yours