To determine the percentage of regular grade gasoline that sells for between $3.22 and $3.62 per gallon, we can use the Empirical Rule (also known as the 68-95-99.7 Rule) which applies to bell-shaped (normal) distributions.

Given:

• Mean (μ): $3.42
• Standard deviation (σ): $0.10
• Range: $3.22 to $3.62

Steps:

1. Calculate the z-scores for the boundaries of $3.22 and $3.62.

   $z_1 = \frac{3.22 - 3.42}{0.10} = \frac{-0.20}{0.10} = -2$ $z_2 = \frac{3.62 - 3.42}{0.10} = \frac{0.20}{0.10} = 2$

2. Interpret the z-scores:

   • A z-score of -2 corresponds to 2 standard deviations below the mean.
   • A z-score of 2 corresponds to 2 standard deviations above the mean.

3. Apply the Empirical Rule:

   • According to the rule, approximately 95% of the data in a normal distribution falls within 2 standard deviations of the mean.

Therefore, 95% of regular grade gasoline sells for between $3.22 and $3.62 per gallon.

Would you like more details or have any questions?

Related Questions:

1. What is the percentage of gasoline prices that fall between $3.32 and $3.52?
2. How much of the gasoline is expected to be priced above $3.62 per gallon?
3. What is the price range that captures 68% of the gasoline prices?
4. How would the percentage change if the standard deviation were $0.20 instead of $0.10?
5. Can you determine the percentage of gasoline prices below $3.22?

Tip:

When working with normal distributions, understanding how to calculate and interpret z-scores is key to finding probabilities and percentages for specific ranges.