Question

suppose the commute times for employees of a large company follow a normal distribution. if the mean time is 18 minutes and the standard deviation is 5 minutes, 95% of the employees will have a travel time within which range A. 13 mins to 23 mins B. 3 mins to 33 mins c 8mins to 28 mins D 13.25 and 22.75

Answer 1

C. 8 mins to 28 mins.

Explanation:

In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean.

In this case, the mean μ commute time is 18 minutes and the standard deviation σ is 5 minutes. Therefore:

• μ = 18 minutes
• σ = 5 minutes

Therefore, two standard deviations below and above the mean would be:

`\boxed{\begin{aligned}\mu - 2\sigma& = 18 - 2(5)\\&=18-10\\&=8\; \sf minutes\end{aligned}}\qquad\qquad \boxed{\begin{aligned}\mu + 2\sigma& = 18 + 2(5)\\&=18+10\\&=28\; \sf minutes\end{aligned}}`

So, 95% of the employees will have a travel time within the range of 8 minutes to 28 minutes.