Question

The diameter of a pipe is normally distributed, with a mean of 0.6 inch and a variance of 0.0016. What is the probability that the diameter of a randomly selected pipe will exceed 0.68 inch?

Answer 1

To find the probability that the diameter of a randomly selected pipe will exceed 0.68 inch, we need to calculate the z-score and use the standard normal distribution table. The z-score is calculated using the formula z = (x - mean) / standard deviation. Finally, we use the standard normal distribution table to find the probability associated with the z-score.

Step-by-step explanation:

To find the probability that the diameter of a randomly selected pipe will exceed 0.68 inch, we need to calculate the z-score and use the standard normal distribution table.

First, we calculate the z-score using the formula: z = (x - mean) / standard deviation. In this case, x = 0.68 inch, mean = 0.6 inch, and standard deviation = sqrt(variance) = sqrt(0.0016) = 0.04 inch.

Plugging in these values, we get z = (0.68 - 0.6) / 0.04 = 0.2 / 0.04 = 5.

Now, we can use the standard normal distribution table to find the probability associated with a z-score of 5. The table gives us that the probability is approximately 1 for z = 5. Therefore, the probability that the diameter of a randomly selected pipe will exceed 0.68 inch is 1.