Final answer:
To find the minimum weight included in the top 5% of the distribution, use the z-score formula and a z-table or calculator to find the corresponding z-value. Then, rearrange the z-score formula to solve for the minimum weight.
Step-by-step explanation:
To find the minimum weight that would be included in the top 5%, we need to find the z-score that corresponds to the top 5% of the normal distribution. The z-score represents the number of standard deviations a particular value is from the mean. We can use the z-score formula:
z = (x - mean) / standard deviation
To find the z-score for the top 5%, we look up the corresponding z-value in the z-table or use a calculator. In this case, the z-value for the top 5% is approximately 1.645.
Now, we can solve for the minimum weight by rearranging the z-score formula:
x = mean + (z * standard deviation)
Plugging in the values, we have:
x = 12.4 + (1.645 * 3) ≈ 17.935
Therefore, the minimum weight that would be included in the top 5% is approximately 17.935 pounds.