Question

Xfinity claims that the performance package for the internet will get you a download speed of 100Mbps. In reality, each person who pays for that package has a slightly different internet speed. For a large data set of performance internet customers, the mean internet speed is 100Mbps, with extended deviation of 8Mbps. As soon as that the internet speeds in the data set can be modeled by a normal distribution.

What percent of Performance Package internet customers would be expected to have internet speeds between 84Mbps and 116Mbps? Be sure to also explain your process of getting the answer. Also, please show your work. ​

Answer 1

Answer: 95%

Explanation:

mean = 100, standard deviation (sd) = 8

mean ± 1 sd = z-score of 1 which is 68%

100 ± 8 = 92 to 108

mean ± 2 sd = z-score of 2 which is 95%

100 ± 2(8) = 84 to 116

mean ± 3 sd = z-score of 3 which is 99.7%

100 ± 3(8) = 76 to 124

The internet speeds are between 84 and 118 which is 2 standard deviations from the mean, which is 95% of their internet customers.