High School

Another cold rolling machine, Machine L, was recently calibrated so that the mean length produced ([tex]\mu[/tex]) is 38.1 mm and the standard deviation of the length ([tex]\sigma[/tex]) is 1 mm. Calculate the probability that the length of a randomly selected bolt from Machine L is 37.5 mm or less.

Answer :

The calculated probability is 0.2743, or 27.43%.

To find the probability that the length of a randomly selected bolt from Machine L is 37.5 mm or less, we can use the z-score formula and standard normal distribution.

Calculate the z-score using the formula:

z = (x - μ) / σ

Substitute the given values into the formula:

z = (37.5 - 38.1) / 1

Calculate the z-score:

z = -0.6

Find the probability using the z-table or a calculator:

P(z ≤ -0.6)

The probability can be determined by looking up the z-score in a standard normal distribution table, which gives us P(z ≤ -0.6) = 0.2743.

Therefore, the probability that the length of a randomly selected bolt from Machine L is 37.5 mm or less is 0.2743, or 27.43%.

Learn more about Probability here:

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