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Suppose that the mean retail price per gallon of regular grade gasoline in the United States is $3.41 with a standard deviation of $0.20 and that the retail price per gallon has a bell-shaped distribution.

(a)
What percentage of regular grade gasoline sold between $3.21 and $3.61 per gallon?
____ %
(b)
What percentage of regular grade gasoline sold between $3.21 and $3.81 per gallon?
______%
(c)
What percentage of regular grade gasoline sold for more than $3.81 per gallon?
_______%

1 Answer

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Answer and Step-by-step explanation:

To find the percentage of regular grade gasoline sold within certain price ranges, we can use the concept of z-scores and the standard normal distribution. The z-score measures the number of standard deviations a value is from the mean.

Given:

Mean (μ) = $3.41

Standard Deviation (σ) = $0.20

(a) To find the percentage of regular grade gasoline sold between $3.21 and $3.61 per gallon:

Step 1: Calculate the z-scores for the lower and upper price limits.

z1 = (3.21 - 3.41) / 0.20

z2 = (3.61 - 3.41) / 0.20

Step 2: Look up the corresponding cumulative probabilities for the z-scores in the standard normal distribution table.

Let's assume z1 = -1.00 and z2 = 1.00 (approximate values from the table).

Step 3: Calculate the percentage.

Percentage = (Cumulative probability for z2 - Cumulative probability for z1) * 100

(b) To find the percentage of regular grade gasoline sold between $3.21 and $3.81 per gallon, follow the same steps as in part (a), using z-scores for the new price limits.

(c) To find the percentage of regular grade gasoline sold for more than $3.81 per gallon:

Step 1: Calculate the z-score for the price limit.

z = (3.81 - 3.41) / 0.20

Step 2: Look up the corresponding cumulative probability for the z-score in the standard normal distribution table.

Step 3: Calculate the percentage.

Percentage = (1 - Cumulative probability for z) * 100

Please note that the specific z-scores and cumulative probabilities from the standard normal distribution table may vary slightly based on the level of precision required.

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