You work for a consumer watchdog publication and are testing the advertising cla

Question

You work for a consumer watchdog publication and are testing the advertising claims of a tire manufacturer. The manufacturer claims that the life spans of the tires are normally distributed, with a mean of 40,000 miles and a standard deviation of 3500 miles. You test 16 tires and get the following life spans. Complete parts (a) through (c) below 47.050 42.470 29.5/5 35.189 30.338 41391 39 859 37.916 25.44 1 31.199 34.465 36,806 30.60? 35 459 37.040 46.197 Is it reasonable to assume that the life spans arc normally distributed Why? Choose the correct answer below. Find the mean of your sample. The mean is 36,248.6 (Round to one decimal place as needed) Find the standard deviation of your sample The standard deviabon is squarebox (Round to one decimal place as needed)

Explanation / Answer

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    579977      
As n =    16      
Thus,          
X =    36248.5625      
          
Setting up tables,          

          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    16      
          
s^2 =    35818370.13      
          
Thus,          
          
s =    5984.845038   [ANSWER, STANDARD DEVIATION]  

x x - X (x - X)^2 47050 10801.44 1.17E+08 42470 6221.438 38706285 29575 -6673.56 44536436 35169 -1079.56 1165455 30338 -5910.56 34934749 41391 5142.438 26444663 39859 3610.438 13035259 37916 1667.438 2780348 25441 -10807.6 1.17E+08 31199 -5049.56 25498081 34465 -1783.56 3181095 36806 557.4375 310736.6 30602 -5646.56 31883668 35459 -789.563 623408.9 37040 791.4375 626373.3 45197 8948.438 80074534

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