A mountain

A mountain climber plans to buy some rope to use as lifeline. Which of the following would be the better choice? Explain your choice.
Rope A: Mean breaking strength:500lb; standard deviation of 100lb
Rope B: Mean breaking strength: 500lb; standard deviation of 10lb

Result

x = (Correct answer is: B)

Solution:

$$\begin{gathered} m_1=500\text{ lb } \\ {s}_1=100\text{ lb } \\ {m}_2=500\text{ lb } \\ {s}_2=10\text{ lb } \\ {p}_1=p(N,m_1,s_1,x<490)=0.4602 \\ {p}_2=p(N,m_2,s_2,x<490)=0.1587 \\ {p}_1>p_2 \\ x=B \end{gathered}$$

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Showing 1 comment:

Dr Math

B - rope with lower std.deviation is better quality;

There is a lower probability that rope break, i.e. at 490 lb with a lower standard deviation than a rope with higher standard deviation.

https://www.hackmath.net/en/calculator/normal-distribution?mean=500&sd=10&above=&area=below&below=490&ll=&ul=&outsideLL=&outsideUL=&draw=Calculate
https://www.hackmath.net/en/calculator/normal-distribution?mean=500&sd=100&above=&area=below&below=490&ll=&ul=&outsideLL=&outsideUL=&draw=Calculate

3 months ago  Like

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