the scores of a high school entrance exam are approximately normally distributed with a given mean $mu =…

the scores of a high school entrance exam are approximately normally distributed with a given mean $mu = 82.4$ and standard deviation $sigma = 3.3$. what percentage of the scores are between 75.8 and 89?\n68%\n95%\n99.7%\n100%

the scores of a high school entrance exam are approximately normally distributed with a given mean $mu = 82.4$ and standard deviation $sigma = 3.3$. what percentage of the scores are between 75.8 and 89?\n68%\n95%\n99.7%\n100%

Answer

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$. For $x = 75.8$, $z_1=\frac{75.8 - 82.4}{3.3}=\frac{- 6.6}{3.3}=- 2$. For $x = 89$, $z_2=\frac{89 - 82.4}{3.3}=\frac{6.6}{3.3}=2$.

Step2: Use the empirical rule

In a normal distribution, approximately 95% of the data lies within $z=-2$ and $z = 2$.

Answer:

95%