Question

The diameters of ball bearings are distributed normally. the mean diameter is 89 millimeters and the standard deviation is 5 millimeters. find the probability that the diameter of a selected bearing is between 85 and 94 millimeters. round your answer to four decimal places.

Answer 1

To calculate the probability of a ball bearing's diameter being between 85 and 94 mm, convert the diameters to Z-scores, find the area under the standard normal distribution for each, and subtract the smaller from the larger area value.

Step-by-step explanation:

To find the probability that the diameter of a selected ball bearing is between 85 and 94 millimeters, given that the mean diameter is 89 millimeters and the standard deviation is 5 millimeters, we use the standard normal distribution.

First, we calculate the Z-scores for both 85 and 94 millimeters:

1. Z for 85 mm = (85 - 89) / 5 = -0.8
2. Z for 94 mm = (94 - 89) / 5 = 1.0

Next, we consult standard normal distribution tables or use a calculator to find the areas under the curve to the left of each Z-score:

• Area to the left of Z = -0.8
• Area to the left of Z = 1.0

To find the probability that the diameter is between 85 and 94 millimeters, we subtract the smaller area from the larger area.

The probability is the difference between these two area values, rounded to four decimal places.