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If bolt thread length is normally distributed, calculate the following proba- bilities: (1) (2 points) The probability that the bolt thread length is within 1.5 2) (4 points) The probability that the bolt thread length is farther than (3) (4 points) The probability that the bolt thread length is between one standard deviations from the expected value. 2.5 standard deviations from the expected value. standard deviation and 2 standard deviations from the expected value.

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Answer #1

A bolt threads length (a) is normally distributed. The thread length of a randomly selected bolt lies 1.5ơ of its mean intercept, as the thread length lies between μ-1.5σ and μ 1.5. The probability is calculated as: =P(-1.5 < z < 1.5) = 29(15)-1 Use Excel to calculate the probability for the Z-Value 1.5. The screenshot of the formula used is shown: 0 Otherwise Thus P(μ-1.5ơ < z < μ + 1.5ơ)-2x 0.9331928-1 = 0.8663856 0.8664

The probability that the thread length of a bolt lies within 1.5σ from the expected value is approximately 0.8664.

The probability that the thread length of a bolt is further than 2.5σ from the expected value is approximately 0.0124.

The probability of the bolt thread length between σ and 2σ from the expected value is 0.271811.

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