Answer:
Approximately 95% of the numbers of days will be between 26 and 58.
Step-by-step explanation:
We are given the following in the question:
Mean, μ = 42
Standard Deviation, σ = 8
We are given that the distribution of average number of days between a bill is a bell shaped distribution that is a normal distribution.
Empirical Formula:
- According to Empirical formula almost all the data lies within three standard deviation of man for a normal distribution.
- Almost 68% of data lies within 1 standard deviation of mean.
- Almost 95% of data lies within two standard deviation of mean.
- Almost 99.7% of data lies within three standard deviation of mean.
Thus, by Empirical formula 95% of data lies within two standard deviation.
![\mu \pm 2(\sigma) \\=42 \pm 2(8)\\=42 \pm 16\\=(26, 58)](https://tex.z-dn.net/?f=%5Cmu%20%5Cpm%202%28%5Csigma%29%20%5C%5C%3D42%20%5Cpm%202%288%29%5C%5C%3D42%20%5Cpm%2016%5C%5C%3D%2826%2C%2058%29)
Thus, approximately 95% of the numbers of days will be between 26 and 58.