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Title: where do we expect a number of jobs to fall most of the time Post by: Hcrutcher2017 on Dec 4, 2017 A small computer center has found that the number of jobs submitted per day to its computers has a mean of 65 jobs and a standard deviation of 7 where do we expect a number of jobs per day to fall most of the time (95.4%)?
Title: Re: where do we expect a number of jobs to fall most of the time Post by: bio_man on Dec 4, 2017 Hi there
I think this question relates to z-score, if I'm not mistaken. Where \(z=\frac{x-μ}{σ}\) \(0.954=\frac{x-65}{7}\) \(0.954\left(7\right)=x-65\) \(0.954\left(7\right)+65=x\) \(0.954\left(7\right)+65=71.678\) Title: Re: where do we expect a number of jobs to fall most of the time Post by: doubleu on Dec 4, 2017 Let's denote the confidence interval as (L,U) where "L" is the lower limit of the confidence interval and "U" is the upper limit of the confidence interval
It's very helpful to remember that within 2 standard deviations of the mean lies \(95.4 %\) of the population. So this means that \(z=2\) (see below) The simplest way to produce a confidence interval is to use the formulas \(L=μ-zσ\) and \(U=μ + zσ\) where \(μ\) is the mean and sigma is the standard deviation, and "z" is the number of standard deviations away from the mean (ie the z score). Note: there are other ways to calculate the confidence interval So \(L=65-2(7)=51\) and \(U=65+2(7)=79\) which means that our confidence interval is (51,79) Title: Re: where do we expect a number of jobs to fall most of the time Post by: bio_man on Dec 4, 2017 My answer is wrong, thanks doubleu
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