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.