A cold drink bottling plant fills bottles of 500 ml. capacity with mean of 500 ml. and a standard deviation of 5 ml. At least what percentage of bottles would contain cold drink between 490 ml. and 510 ml.?

Correct option is B

Step 1: Identify the parameters:

• Mean (μ) = 500 ml

• Standard deviation (σ) = 5 ml

• Range of interest: 490 ml to 510 ml

Step 2: Calculate how many standard deviations away 490 ml and 510 ml are from the mean.

So, the range 490 ml to 510 ml corresponds to Z = -2 to Z = +2 on the standard normal distribution.

Step 3: Use the Empirical Rule or standard normal distribution table:

• The Empirical Rule states:

  • About 68.27% of data lies within ±1σ

  • About 95.45% of data lies within ±2σ

  • About 99.73% of data lies within ±3σ

Between Z = -2 and Z = +2, the percentage of data is approximately 95.45%.

Since 490 ml and 510 ml correspond to ±2 standard deviations from the mean, the percentage of bottles filled between these volumes is approximately 95%.

Information Booster:

• The Empirical Rule applies to bell-shaped normal distributions.

• According to this rule:

  • ~68% of values lie within ±1σ

  • ~95% lie within ±2σ

  • ~99.7% lie within ±3σ

• In this question, since the range is within ±2σ, the correct percentage is 95%.

• ​This helps quality control departments in estimating product consistency.
• Useful in production and inventory forecasting in operations management.