Question

Freespace is a popular form of social media. Recent reports show that the mean time spent on the app is 35 minutes a day with a standard deviation of 7 minutes a day. The data is normally distributed. If 6900 people are on in one sitting how many of them lie within one standard deviation below the mean and three stand deviations above the mean? *Round to the nearest whole value*

Answer 1

Recall the 68-95 - 99.7 rule of the area of the normal curve. See the illustration below.

As we can see above, the percentage of data that lies within one standard deviation below the mean is 34.13%.

On the other hand, from the center 0 to +3SD, the percentage of data that lies within this interval is 34.13% + 13.59% + 2.14% = 49.86%

Hence, the percentage of data that lies from 1SD below the mean to 3SD above the mean is 34.13% + 49.86% = 83.99% or 84% .

Let's determine how many people of the 6,900 composed the 84% by multiplying 6,900 by 0.84

`6,900*0.84=5,796`

Therefore, 5, 796 people lie within one standard deviation below the mean and three stand deviations above the mean.