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Lapatulllka [165]
3 years ago
7

The breaking strength of a cable is assumed to be lognormally distributed with a mean of 75 and standard deviation of 20. • If t

he load of magnitude 50 is hung from the cable, determine the probability of failure of the cable? • If the load can take values 30, 50, and 70 with probabilities 0.2, 0.35, and 0.45 respectively, determine the probability of failure of the cable?
Mathematics
1 answer:
son4ous [18]3 years ago
3 0

Answer:

If the load of magnitude 50 is hung from the cable, determine the probability of failure of the cable?

There is a 10.56% probability of failure of the cable.

If the load can take values 30, 50, and 70 with probabilities 0.2, 0.35, and 0.45 respectively, determine the probability of failure of the cable?

There is a 15.87% probability of failure of the cable.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

The breaking strength of a cable is assumed to be lognormally distributed with a mean of 75 and standard deviation of 20. This means that \mu = 75, \sigma = 20.

If the load of magnitude 50 is hung from the cable, determine the probability of failure of the cable?

This is the pvalue of Z when X = 50.

Z = \frac{X - \mu}{\sigma}

Z = \frac{50 - 75}{20}

Z = -1.25

Z = -1.25 has a pvalue of 0.1056.

There is a 10.56% probability of failure of the cable.

If the load can take values 30, 50, and 70 with probabilities 0.2, 0.35, and 0.45 respectively, determine the probability of failure of the cable?

Now we have that

X = 0.2(30) + 0.35(50) + 0.45(70) = 55

Z = \frac{X - \mu}{\sigma}

Z = \frac{55 - 75}{20}

Z = -1

Z = -1 has a pvalue of 0.1587.

There is a 15.87% probability of failure of the cable.

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Answer:

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Step-by-step explanation:

Since Chelsea bought a computer on Monday for $ 1,300, and its value is predicted to decrease by $ 250 per year, while her brother George also bought a computer on Monday, and the function g (x) = 1,100 - 175x predicts how the value of his computer is expected to change after x years, to determine whose computer is expected to have a greater value when it is 3 years old, and how much greater will it be, the following calculation must be performed:

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