The distribution of hourly sales for a local family owned store is normally distributed with a mean of $225 per hour and a standard deviation of $75 per hour. Which of the following intervals contains the middle 95% of hourly sales
Question
The distribution of hourly sales for a local family owned store is normally distributed with a mean of 75 per hour. Which of the following intervals contains the middle 95% of hourly sales
Solution 1
To find the interval that contains the middle 95% of hourly sales, we need to use the properties of the normal distribution.
In a normal distribution, about 95% of the data falls within two standard deviations of the mean.
So, to find this interval, we calculate as follows:
- Lower limit: Mean - 2*Standard Deviation = 75 = $75
- Upper limit: Mean + 2*Standard Deviation = 75 = $375
So, the interval that contains the middle 95% of hourly sales is $
Solution 2
The middle 95% of a normally distributed set of data falls within approximately 2 standard deviations of the mean. This is part of the empirical rule or 68-95-99.7 rule.
Here's how to calculate the interval:
- Multiply the standard deviation by 2: 75 * 2 = 150
- Subtract this value from the mean for the lower bound of the interval: 225 - 150 = 75
- Add this value to the mean for the upper bound of the interval: 225 + 150 = 375
So, the middle 95% of hourly sales should fall between 375.
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