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Delivery times follow a normal distribution with mean 70 minutes and standard deviation 5 minutes. About what share of deliveries take between 65 and 75 minutes?
AAbout 68%
BAbout 95%
CAbout 75%
DAbout 50%
Answer & Solution
Correct answer: A. About 68%
1. The interval from 65 to 75 minutes is the mean of 70 plus or minus one standard deviation of 5.
2. For a normal distribution, the Empirical Rule gives the share of data within fixed numbers of standard deviations.
3. Within one standard deviation of the mean lies approximately 68% of the data.
4. So about 68% of deliveries take between 65 and 75 minutes.
5. Option B, 95%, is the share within two standard deviations, the band from 60 to 80 minutes.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.7 Measures of the Spread of the Data_
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