Question

The amount of juice dispensed from a machine is normally distributed with a mean of 10.50 ounces and a standard deviation of 0.75 ounce. Which interval represents the amount of juice dispensed about 68% of the time?(1 point)
Responses

9.75–11.25
9.75–11.25

9.75–10.5
9.75–10.5

10.5–11.25
10.5–11.25

9–12

Answer 1

In a normal distribution, approximately 68% of the data falls within one standard deviation from the mean.

Given:
- Mean (μ) = 10.50 ounces
- Standard deviation (σ) = 0.75 ounces

To find the range that contains about 68% of the juice dispensed, we calculate:
- Lower limit: μ - σ = 10.50 - 0.75 = 9.75 ounces
- Upper limit: μ + σ = 10.50 + 0.75 = 11.25 ounces

Thus, the interval that represents the amount of juice dispensed about 68% of the time is **9.75–11.25**.