Step 1: Define the Given Values

• Mean (μ) = 500 ml

• Standard deviation (σ) = 5 ml

• Range: 490 ml to 510 ml

  • Distance from the mean:

    490 = 500 − 10 (which is −2σ)
    $$510=500+10\text{(which is +2σ)}$$

  • So, this range represents within 2 standard deviations (k = 2).

• Assuming Normal Distribution
  If the volume follows a normal distribution, we can use the empirical rule (68-95-99.7 rule):

  • Within 2 standard deviations of the mean: ≈95.4% of values fall within this range.