To solve this probability problem, we can approach it using the properties of the normal distribution.

Given Information:

• The mean diameter of bolts, $\mu = 0.30$ inches.
• The standard deviation, $\sigma = 0.01$ inches.
• We are asked to find the probability that a bolt's diameter is greater than 0.32 inches.

Solution:

1. Convert to Z-score: $Z = \frac{X - \mu}{\sigma}$ where $X = 0.32$, $\mu = 0.30$, and $\sigma = 0.01$.

   $Z = \frac{0.32 - 0.30}{0.01} = \frac{0.02}{0.01} = 2$

2. Find the Probability: We want to find $P(X > 0.32)$, which is equivalent to finding $P(Z > 2)$.

   Using a standard normal distribution table or calculator, we find: $P(Z > 2) \approx 0.0228$

Conclusion:

Approximately 2.28% of bolts will have a diameter greater than 0.32 inches.

Would you like further details or have any questions?

Here are some related questions for further practice:

1. What percentage of bolts have a diameter less than 0.28 inches?
2. What percentage of bolts have a diameter between 0.29 and 0.31 inches?
3. If the standard deviation changed to 0.02 inches, what would be the new percentage of bolts with diameters greater than 0.32 inches?
4. What is the probability that a bolt has a diameter exactly equal to the mean?
5. How would the probability change if the mean diameter were 0.31 inches instead?

Tip: For normal distribution problems, always standardize the values by converting them to Z-scores for easier probability lookup.