The test scores from a recent Mathematics test are as follows: 95.5,65.9,93.2,88.6,56.8,50,86.4,54.5,40.9,77.3,79.5,65.9,70.5,77.3,81.8,50,79.5,and 68.2.The mean score was 71.2 with a standard deviation of 15.5.If the Normal model is appropriate,what percent of the scores will be less than 40.2?
A)0.15%
B)10%
C)5%
D)15.87%
E)2.28%

Question

Quizplus · Accepted Answer

To find the percentage of scores less than 40.2, we use the z-score formula: $z = \frac{x - \mu}{\sigma}$, where $x$ is the value in question, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the given values: $z = \frac{40.2 - 71.2}{15.5} = -2$. Looking up a z-score of -2 in a standard normal distribution table or using a calculator gives an area (or percentage) of approximately 2.28% to the left of $z = -2$, which represents the percentage of scores less than 40.2.

The Test Scores from a Recent Mathematics Test Are as Follows