Answer:
About 95% of data lies between 15.6 and 32.4
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 2.4
Standard Deviation, σ = 4.2
We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.
Empirical Formula:
- Almost all the data lies within three standard deviation from the mean for a normally distributed data.
- About 68% of data lies within one standard deviation from the mean.
- About 95% of data lies within two standard deviations of the mean.
- About 99.7% of data lies within three standard deviation of the mean.
We have to find the percentage of data lying between 15.6 and 32.4
![15.6 = 24 - 2(4.2) = \mu - 2\sigma\\32.4 = 24 + 2(4.2) = \mu + 2\sigma](https://tex.z-dn.net/?f=15.6%20%3D%2024%20-%202%284.2%29%20%3D%20%5Cmu%20-%202%5Csigma%5C%5C32.4%20%3D%2024%20%2B%202%284.2%29%20%3D%20%5Cmu%20%2B%202%5Csigma)
Thus, we have to find the percentage of data lying within two standard deviations of the mean. By Empirical formula about 95% of data lies between 15.6 and 32.4