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Demand for stereo headphones and MP3 players for joggers has caused Nina Industries to grow almost 50 percent over the past year. The number of joggers continues to expand, so Nina expects demand for headsets to also expand, because, as yet, no safety laws have been passed to prevent joggers from wearing them. Demand for the players for last year was as follows:

Month	Demand (units)
January	4200
February	4300
March	4000
April	4400
May	5000
June	4700
July	5300
August	4900
September	5400
October	5700
November	6300
December	6000

b. To be reasonably confident of meeting demand, Nina decides to use three standard errors of estimate for safety. How many additional units should be held to meet this level of confidence?

Step by step solution

01

Definition of the standard error of estimate

Thestandard error of an estimate is the estimate of the standard deviation of the error term. The standard error of a statistic is the variance of a sample population. the standard error could be a term that measures the accuracy with which a distribution represents a population by using a variance. The mean is derived from the actual mean of a population; this deviation is known as the standard error of the mean.

02

Explanation

The three standard errors of the estimate for safety and additional units held to meet the level of confidence are as follows:

${\mathrm{S}}_{\mathrm{yt}}=\frac{\sqrt{{\mathrm{Î\pounds }}_{\mathrm{i}=1}^{\mathrm{n}}}{\left(\mathrm{yi}-\mathrm{Yi}\right)}^2}{\mathrm{n}-2}=\sqrt{\frac{728205.128}{12-2}}=269.85$

Therefore, 3 standard errors of the estimate would be 3(269.85) = 809.55 = 810

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