According to the South Dakota Department of Health, the mean number of hours of

Question

According to the South Dakota Department of Health, the mean number of hours of TV viewing per week is higher among adult women than men. A recent study showed women spent an average of 34 hours per week watching tv and men 29 hours per week. Assume that the distribution of hours watched follows the normal distribution for both groups, and that the standard deviation among the women is 4.5 hours and is 5.1 hours for the men.

Find the number of hours of tv watching for women that divides the top 5% from the bottom 95%.

Explanation / Answer

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.95      
          
Then, using table or technology,          
          
z =    1.644853627      
          
As x = u + z * s,          
          
where          
          
u = mean =    34      
z = the critical z score =    1.644853627      
s = standard deviation =    4.5      
          
Then          
          
x = critical value =    41.40184132   [ANSWER]  

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