Suppose the commute times for employees of a large company follow a normal distribution. If the mean time is 22 minutes and the standard deviation is 5 minutes, 95% of the employees will have a travel time within which range?A.17.25 minutes to 26.75 minutesB.17 minutes to 27 minutesC.12 minutes to 32 minutesD.7 minutes to 37 minutesSUBMITarrow_backPREVIOUS
Question
Suppose the commute times for employees of a large company follow a normal distribution. If the mean time is 22 minutes and the standard deviation is 5 minutes, 95% of the employees will have a travel time within which range?A.17.25 minutes to 26.75 minutesB.17 minutes to 27 minutesC.12 minutes to 32 minutesD.7 minutes to 37 minutesSUBMITarrow_backPREVIOUS
Solution
To determine the range within which 95% of the employees' commute times fall, we need to use the properties of the normal distribution. Specifically, we will use the fact that 95% of the data in a normal distribution lies within approximately 1.96 standard deviations from the mean.
Given:
- Mean (μ) = 22 minutes
- Standard deviation (σ) = 5 minutes
Step-by-step solution:
-
Calculate the range for 95% of the data:
- Lower bound: μ - 1.96σ
- Upper bound: μ + 1.96σ
-
Substitute the given values into the formulas:
- Lower bound: 22 - 1.96 * 5
- Upper bound: 22 + 1.96 * 5
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Perform the calculations:
- Lower bound: 22 - 9.8 = 12.2 minutes
- Upper bound: 22 + 9.8 = 31.8 minutes
Therefore, 95% of the employees will have a travel time within the range of approximately 12.2 minutes to 31.8 minutes. The closest answer choice to this range is:
C. 12 minutes to 32 minutes
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