SOLUTION: Applying the 68- 95- 99.7 Rule. When designing the placement of a CD player in a new model car, engineers must consider the forward grip reach of the driver. Women have forward gri

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Question 839129: Applying the 68- 95- 99.7 Rule. When designing the placement of a CD player in a new model car, engineers must consider the forward grip reach of the driver. Women have forward grip reaches that are normally distributed with a mean of 27.0 inches and a standard deviation of 1.3 inches (based on anthropometric survey data from Gordon, Churchill et al.). Use the 68- 95- 99.7 rule to find the indicated quantity.
a. Find the percentage of women with forward grip reaches between 24.4 inches and 29.6 inches.
b. Find the percentage of women with forward grip reaches less than 30.9 inches.
c. Find the percentage of women with forward grip reaches between 27.0 inches and 28.3 inches.
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

27.0 inches and a standard deviation of 1.3 inches 

Usimg the 68- 95- 99.7



a. Find the percentage of women with forward grip reaches between 24.4 inches and 29.6 inches. 95%

 b. Find the percentage of women with forward grip reaches less than 30.9 inches.50+%2B+99.7%2F2  = 99.85%

 c. Find the percentage of women with forward grip reaches between 27.0 inches and 28.3 inches. 68%2F2 = 34%



For the normal distribution: 

one  standard deviation from the mean accounts for about 68.2% of the set 

two standard deviations from the mean account for about 95.4%

and three standard deviations from the mean account for about 99.7%.