SOLUTION: 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 dist

Question 331603: 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.Use the 68-95-99.7 rule to find:
A) 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 jrfrunner(365) (Show Source): You can put this solution on YOUR website!
Given Normally distributed data with mean=27.0 and standard deviation =1.3
1 standard deviation = 1.3
2 standard deviations=2.6
3 standard deviations =3.9
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A) The percentage of women with forward grip reaches between 24.4 inches and 29.6 inches.
compute the mid-range
Upper value-Xbar =29.6-27.0=2.6
Xbar - Lower value =27.0-24.4=2.6
This means that 24.4 to 29.6 is 2 standard deviations from the mean
approximately 95% of the data will lie within 2 standard dev from the mean
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B) Find the percentage of women with forward grip reaches less than 30.9 inches.
----
compute the distance in standard deviations from the mean to the largest value
30.9-27.0 = 3.9 this is 3 standard deviations above the mean
1/2 of 99.7% of the data will lie within the mean and 3 standard deviations
50% of the data will lie below the mean
so, the answer is 50% + 1/2*99.7% =99.85%
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C) Find the percentage of women with forward grip reaches between 27.0 inches and 28.3 inches.
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compute the distance which starts at the mean 27.0 and goes to 28.3
28.3-27.0=1.3 this is one standard deviation above the mean
Since approx 68% of the data lies within 1 standard deviation on either side of the maan, the answer is 1/2* 68% = 34%

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