The diameters of ball bearing are distributed normally. The mean diameter is 138 millimeters and the variance is 9. Find the probability that the diameter of a selected bearing is greater than 132 millimeters

97.72% probability that the diameter of a selected bearing is greater than 132 millimeters

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation(which is the square root of the variance) , the zscore of a measure X is given by:

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 question:

Find the probability that the diameter of a selected bearing is greater than 132 millimeters

This is 1 subtracted by the pvalue of Z when X = 132. So

has a pvalue of 0.0228

1 - 0.0228 = 0.9772

97.72% probability that the diameter of a selected bearing is greater than 132 millimeters

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