Question #341504

The amount of material used in making a custom sail for a sailboat is normally distributed with a standard deviation of 64 square feet. For a random sample of 15 sails, the mean amount of material used is 912 square feet. Find a 90% confidence interval for the population mean amount of material used in a custom sail.

  1. Point estimate value = 
  2. Standard error (approximate to four decimal points) = 
  3. Margin of error (approximate to four decimal points) = 
  4. Tabulated value (approximate to four decimal points) = 
  5. Upper limit (approximate to four decimal points) = 
  6. Lower limit (approximate to four decimal points) = 
1
Expert's answer
2022-05-16T17:54:32-0400

1. Point estimate value = 


xˉ=912/15=60.8\bar{x}=912/15=60.8



2. Standard error (approximate to four decimal points) = 


SE=σ/n=64/15=16.5247SE=\sigma/\sqrt{n}=64/\sqrt{15}=16.5247

3. Margin of error (approximate to four decimal points) = 


M=zα/2×SE=1.6449×6415=27.1815M=z_{\alpha/2}\times SE=1.6449\times\dfrac{64}{\sqrt{15}}=27.1815

4. Tabulated value (approximate to four decimal points) = 


zα/2=1.6449z_{\alpha/2}=1.6449


5. Upper limit (approximate to four decimal points) = 


60.8+16.5247=77.324760.8+16.5247=77.3247

6. Lower limit (approximate to four decimal points) = 


60.816.5247=44.275360.8-16.5247=44.2753

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