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Pressure in Pascals for high heel shoe print

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A high heel shoe leaves a foot print on the floor. The front area part of the print has an area or 32.5 cm squared. The heel of shoe leaves a 1 cm circle imprint. Standing on one leg, what pressure in pascals would you exert on the floor, assuming you weigh 165 lbs?

How deep would one need to dive in fresh water in order to achieve this same pressure? Repeat if you were able to concentrate all your weight on the heel alone?

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Solution. By a formula P=F/S, where P is the pressure, F is the force and S is the corresponding area. We have

(1) If we assume that you were able to concentrate all your weight on a foot, then

P1=165/32.5 lbs/cm^2
=5.077 lbs/cm^2

Since 1 inch=0.3937 cm, we can get 1 cm=2.54 inch

P1=5.077/2.54^2 lbs/inch^2
=0.787 lbs/inch^2

Assume that ...

Solution provided by:
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
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  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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