Question

Scores on a test in a very large class are bell-shaped and symmetric. The mean on the test was 75, and the standard deviation was 5. What percent of the scores were above 75?

Answer 1

Answer:

50% of the scores were above 75

Step-by-step explanation:

Problems of normally distributed(bell-shaped) samples are 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:

$\mu = 75, \sigma = 5$

What percent of the scores were above 75?

This is 1 subtracted by the pvalue of Z when X = 75. So

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

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

$Z = 0$

$Z = 0$ has a pvalue of 0.5

1 - 0.5 = 0.5

50% of the scores were above 75