Answered: Climbing rope will break if pulled hard…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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