Question

The diameters of ball bearings are distributed normally. the mean diameter is 69 69 millimeters and the standard deviation is 4 4 millimeters. find the probability that the diameter of a selected bearing is greater than 62 62 millimeters. round your answer to four decimal places.

Answer 1

To find the probability that the diameter of a selected bearing is greater than 62 millimeters, we need to use the standard normal distribution. The probability is approximately 0.9600.

Step-by-step explanation:

To find the probability that the diameter of a selected bearing is greater than 62 millimeters, we need to use the standard normal distribution. First, we need to convert 62 millimeters to a z-score using the formula z = (x - mean) / standard deviation. Plugging in the values, we get z = (62 - 69) / 4 = -1.75. Next, we need to find the area to the right of -1.75 on the standard normal distribution table. Looking up -1.75 in the z-score table, we find that the area to the left is 0.0401. Therefore, the probability of the diameter of a selected bearing being greater than 62 millimeters is 1 - 0.0401 = 0.9599. Rounded to four decimal places, the probability is approximately 0.9600.