help! statistics (normal distribution)
If a car seat is too low to too high, it will be uncomfortable and possibly dangerous. Most seats are made to be adjustable, so that men and women with different sitting heights can select a comfortable setting. When designing car seats, the sitting knee heights of men and women become very relevant. Men have sitting knee heights that are normally distributed with a mean of 22.0 in. and a standard deviation of 1.1 in.., and women have sitting knee heights that are normally distributed with a mean of 20.3 in. and a standard deviation of 1.0 in. (based on anthropometric survey data from Gordon, Churchill etc. al)
A) Find minimum and maximum sitting knee heights that include at least 95% of all men and at least 95% of all women.. Remember, at least 95% or more.
B) Using your answer from part (a), try to find cost-effective limits that are close together as possible. Remember, there are no separate seats designed for men or women You have to decide what minimum and maximum sitting knee heights you will be using, i.e. choose one minimum and one maximum sitting knee height. Clearly explain your reasoning for choosing your minimum and maximum sitting knee heights.
C) Using the maximum and minimum sitting knee heights from part (b), find the percentage of men with sitting knee heights between the limits you have determined, and then find the percentage of women with sitting knee heights between those limits. Do your limits favor one gender at the expense of the other? Why or Why not? Explain briefly.
D) Why is it not practical to simply design car seats so that they accommodate everyone?
E) If you were a design engineer for General Motors, what percentage would you be willing to exclude in your design of car seats and why? Explain
F) Apart from sitting knee height, what is another important design component that should be considered when determining the adjustment range or car seats?