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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

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zubam2002

Answer:  

The standard deviation of 75 dollars

Explanation:

Standard deviation, S.D.= 75 dollars; Mean, M= 225 dollars; Mean deviation, D= ?

S.D. = √ D² - M

∴ 75 = √ D² - 225

D² = 75² - 225 = 5625 + 225 = 5950

∴ D = √5950 = 24.4 dollars

From the above, it shows that, the standard deviation of 75 dollars contains the middle 95 percent of hourly sales.

fichoh

The interval which contains the middle 95% of hourly sales computed using the empirical relation principle for a normal distribution is $75 to $375

The middle 95% can be interpreted using the empirical relation as being 2 standard deviations from the mean.

Given the Parameters :

  • Mean, μ = $225
  • Standard deviation, σ = $75

The middle 95% equals 2σ from the mean :

Hence, the sales interval can be written as :

  • μ-2σ to 2σ+μ

  • μ-2σ = $225 - (2 × 75) = $225 - $150 = $75

  • 2σ+μ = (2 × $75) + $225 = $150 + $225 = $375

Therefore, the interval which contains the middle 95% of hourly sales is $75 to $375

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