Question

the diameter of a machine part produced by a factory is normally distributed, with a mean of 10 meters and a standard deviation of 2 meters. what is the probability of a part having a diameter of at least 13 meters?

Answer 1

To find the probability of a part having a diameter of at least 13 meters, we can use the standard normal distribution. The probability is approximately 0.0668.

Step-by-step explanation:

To find the probability of a part having a diameter of at least 13 meters, we can use the standard normal distribution.

First, we need to convert 13 meters to a z-score using the formula z = (x - mean) / standard deviation. In this case, the mean is 10 meters and the standard deviation is 2 meters.

So, the z-score is (13 - 10) / 2 = 1.5.

Next, we can use a standard normal distribution table or a calculator to find the probability associated with a z-score of 1.5.

The probability of a part having a diameter of at least 13 meters is the same as the probability of a z-score greater than 1.5. Looking up this value in a standard normal distribution table, we find that the probability is approximately 0.0668.