The load required to degrade the structural integrity of a foundation is normally distributed with a mean of 22 tons and a standard deviation of 5 tons. (a) While at the site, a fellow engineer asks you the approximate probability that it takes between 17 and 27 tons to degrade the foundation. Being knowledgeable in statistics, what you are able to tell him off the top of your head? (b) Verify that your estimate in (a) is accurate using R. (c) A similar foundation is to be constructed so that the load required to degrade its integrity is again normally distributed with a standard deviation of 5 tons, but the improved foundation is required to only have a 20% chance to degrade under a 22 ton load or less. What must the mean of this distribution be so that the foundation is constructed to the given specifications? Use R.
The load required to degrade the structural integrity of a foundation is normally distributed with a
mean of 22 tons and a standard deviation of 5 tons.
(a) While at the site, a fellow engineer asks you the approximate probability that it takes between 17
and 27 tons to degrade the foundation. Being knowledgeable in statistics, what you are able to
tell him off the top of your head?
(b) Verify that your estimate in (a) is accurate using R.
(c) A similar foundation is to be constructed so that the load required to degrade its integrity is again
normally distributed with a standard deviation of 5 tons, but the improved foundation is required
to only have a 20% chance to degrade under a 22 ton load or less. What must the mean of this
distribution be so that the foundation is constructed to the given specifications? Use R.
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