Question

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. Which of the following represents a 99% confidence interval for the population mean amount of material used in a custom sail?
A. 912 ± 46.8
B. 912 ± 42.6
C. 912 ± 44.3
D. 912 ± 49.2

Answer 1

Level of Significance ,    α =    0.01          
'   '   '          
z value=   z α/2=   2.5758   [Excel formula =NORMSINV(α/2) ]      
                  
Standard Error , SE = σ/√n =   64.0000   / √   15   =   16.524729
margin of error, E=Z*SE =   2.5758   *   16.52473   =   42.564881 = 42.6

B. 912 ± 42.6

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