Question

Suppose that the breaking strength of a rope (in pounds) is normally distributed, with a mean of 100 pounds and a standard deviation of 17. What is the probability that a certain rope will break before being subjected to 130 pounds?

Answer 1

To find the probability that a certain rope will break before being subjected to 130 pounds, we use the normal distribution and the z-score formula. The probability is approximately 0.9608, or 96.08%.

Step-by-step explanation:

To find the probability that a certain rope will break before being subjected to 130 pounds, we need to use the normal distribution. The mean breaking strength of the rope is 100 pounds and the standard deviation is 17 pounds. We want to find the probability that the breaking strength is less than 130 pounds, which can be calculated using the z-score formula.

First, we calculate the z-score:

z = (130 - 100) / 17 = 1.76

Next, we use a z-score table or calculator to find the corresponding probability. In this case, the probability is approximately 0.9608, or 96.08%.