Question

The diameters of ball bearings are distributed normally. The mean diameter is 135 millimeters and the variance is 4. Find the probability that the diameter of a selected bearing is greater than 132 millimeters. Round your answer to four decimal places.

Answer 1

0.9332

Explanation:

The variance is 4, so the standard deviation is √4 = 2.

Calculate the z-score:

z = (x − μ) / σ

z = (132 − 135) / 2

z = -1.5

Use a table or calculator to find the probability.

P(Z > -1.5) = 1 − 0.0668

P(Z > -1.5) = 0.9332

Answer 2

To find the probability that the diameter of a selected bearing is greater than 132 millimeters, we need to find the z-score of 132 and use a standard normal distribution table or a calculator. The probability is approximately 0.9332.

To find the probability that the diameter of a selected bearing is greater than 132 millimeters, we need to find the z-score of 132 using the formula: z = (x - mean) / standard deviation.

First, let's find the standard deviation by taking the square root of the variance: standard deviation = sqrt(4) = 2. Now we can calculate the z-score: z = (132 - 135) / 2 = -1.5.

We can then use a standard normal distribution table or a calculator to find the probability that a z-score is greater than -1.5. In this case, the probability is approximately 0.9332, rounded to four decimal places.