2 multiple choice 1 point the scores on an exam are normally distributed, with a mean of 78 and a standard…

2 multiple choice 1 point the scores on an exam are normally distributed, with a mean of 78 and a standard deviation of 6. what percent of the scores are greater than 84? 16% 68% 84% 2.5%

2 multiple choice 1 point the scores on an exam are normally distributed, with a mean of 78 and a standard deviation of 6. what percent of the scores are greater than 84? 16% 68% 84% 2.5%

Answer

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 84$, $\mu=78$, and $\sigma = 6$. So $z=\frac{84 - 78}{6}=\frac{6}{6}=1$.

Step2: Use the properties of the normal distribution

In a normal distribution, about 68% of the data lies within 1 standard - deviation of the mean ($\mu\pm\sigma$), which means that the percentage of data outside of $\mu\pm\sigma$ is $100%-68% = 32%$. Since the normal distribution is symmetric, the percentage of data greater than $\mu+\sigma$ is $\frac{32%}{2}=16%$.

Answer:

16%