g A random sample of size 16 taken from a normally distributed population revealed a sample mean of 50 and a sample variance of 36. The upper limit of a 95% confidence interval for the population mean would equal:

The  upper limit is    

Step-by-step explanation:

From the question we  told that

     The  sample size is

      The sample mean is  

      The sample variance is  

For  a  95% confidence interval the confidence level is  95%

Given that the confidence level is 95% then the level of significance is  mathematically evaluated  as  

Next we obtain the critical value of   from the normal distribution table(reference- math dot armstrong dot edu), the value is  

Generally the margin of error is mathematically represented as

 Here   is the standard deviation which is mathematically evaluated as

substituting values

=>                

So

The 95% confidence interval is mathematically represented as

substituting values

The  upper limit is    

21/58.

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geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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