A piece of rope is made up of 100 strands. Assume that the breaking strength of the rope is the sum of the breaking strengths of the individual strands. Assume further that this sum may be considered to be the sum of an independent trials process with 100 experiments each having expected value of 10 pounds and standard deviation 1. Find the approximate probability that the rope will support a weight of 985 pounds.

• 0.057
• 0.067
• 0.077
• 0.087
• 0.1

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Solution: B

The sum of the breaking strengths is approximately normally distributed with mean 100*10 = 1000 and variance 100. Hence the approximate probability that the rope will support a weight of 985 pounds is approximately the probability that a standard normal exceeds -15/10 = -1.5, which equals 0.9332 .