Sarah is a mechanical engineer working in the shoe industry. One of her clients has asked her to…

Sarah
is a mechanical engineer working in the shoe industry. One of her clients has
asked her to design a machine that can manufacture footwear that will fit 92%
of the shoe-buying public. The accounting wizards from the client’s firm
performed a cost–benefit analysis and determined that the cost of making
footwear for those unlucky 8% brings little benefit. The mean shoe size of the
footwear-buying public is nine units with a standard deviation of three units.
The measurements of foot size are normally distributed.

a.
If the footwear company is concerned with offending the tiny feet
»

Sarah
is a mechanical engineer working in the shoe industry. One of her clients has
asked her to design a machine that can manufacture footwear that will fit 92%
of the shoe-buying public. The accounting wizards from the client’s firm
performed a cost–benefit analysis and determined that the cost of making
footwear for those unlucky 8% brings little benefit. The mean shoe size of the
footwear-buying public is nine units with a standard deviation of three units.
The measurements of foot size are normally distributed.

a.
If the footwear company is concerned with offending the tiny feet lobby by not
accommodating those with small feet (i.e., small shoe sizes are made), what is
the largest shoe size that Sarah’s machine should make (rounding to the nearest
whole size)?

b.
An athletic shoe company specializing in basketball shoes wants Sarah to design
a similar machine to accommodate the larger feet of basketball players;
however, they are still selling to the general public. In this case, the
company still wants to have shoes that fit 92% of the population, but they
don’t want to miss any of the larger sizes. What is the smallest shoe size that
Sarah’s machine should make (rounding to the nearest whole size)?

c.
Lastly, after feeling a bit guilty that only the large-footed or small-footed
individuals were getting neglected, Sarah designed a machine that neglected
both. What are the largest and smallest shoe sizes Sarah’s machine can make to
fit the middle 92% (rounding to the nearest whole size)?

 

»

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