Question

The net weight in pounds of a packaged chemical herbicide is uniform for 49.70 < x < 50.23 pounds.

(a) Determine the mean of X (in pounds) (Round your answer to 2 decimal places.)

Answer 1

The mean (average) of X, the net weight of the packaged chemical herbicide, within the given range of 49.70 to 50.23 pounds is approximately 49.97 pounds.

Step-by-step explanation:

To find the mean (average) of a continuous uniform distribution, you add the lower and upper bounds of the range and divide by 2. In this case, for the range 49.70 < x < 50.23, the mean (μ) can be calculated as follows:

`\[ \text{Mean (} \mu \text{)} = \frac{\text{Lower Bound} + \text{Upper Bound}}{2} \]`

`\[ \mu = (49.70 + 50.23)/(2) \]`

`\[ \mu = (99.93)/(2) \]`

`\[ \mu \approx 49.97 \text{ pounds} \]`

Therefore, the mean net weight of the packaged chemical herbicide is approximately 49.97 pounds within the specified range.

Understanding the mean in a continuous uniform distribution is crucial for describing the central tendency of the data set. It represents a balance point within the given range and provides valuable information about the distribution of weights for the herbicide packages.