Climbing rope will break if pulled hard enough. Experiments show that 10.5 mm dynamic nylon rope has a mean breaking point of 5036 lbs with a standard deviation of 122 lbs. Assume breaking points of rope are normally distributed. Attach your solutions with full working (including any use of R) below. i) Sketch the distribution of breaking points for this rope, clearly labeling important points on the axes. ii) What proportion of ropes will break with exactly 5000 lbs of load? iii) At what load will 95% of all ropes break?

A First Course in Probability (10th Edition)
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Climbing rope will break if pulled hard enough. Experiments show that 10.5 mm dynamic nylon rope has a mean breaking point of 5036 lbs with a standard deviation of 122 lbs. Assume breaking points of rope are normally distributed. Attach your solutions with full working (including any use of R) below.

i) Sketch the distribution of breaking points for this rope, clearly labeling important points on the axes.

ii) What proportion of ropes will break with exactly 5000 lbs of load?

iii) At what load will 95% of all ropes break?

iv) Find how likely it is that such a rope breaks under 1000 lbs of weight.

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