Final Answer:
a) Approximately 68% of gasoline in New York sold between $3.33 and $3.53 per gallon.
b) About 15.87% of gasoline in New York sold for less than $3.23 per gallon.
c) Around 50% of gasoline in New York sold for more than $3.43 per gallon.
d) Roughly 84.13% of gasoline in New York sold for less than $3.63 per gallon.
e) No percentage can be calculated for the range $3.23 to $3.13, as $3.23 is greater than $3.13.
Step-by-step explanation:
a) To find the percentage of gasoline sold between $3.33 and $3.53 per gallon, we refer to the empirical rule for a normal distribution. Since the mean is $3.43 and the standard deviation is $0.10, within one standard deviation of the mean covers approximately 68% of the data. Therefore, the answer is 68%.
b) To determine the percentage of gasoline sold for less than $3.23 per gallon, we need to find the z-score for $3.23 using the formula z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. Once we find the z-score, we can look up the corresponding percentage in the standard normal distribution table. The answer is approximately 15.87%.
c) For the percentage of gasoline sold for more than $3.43 per gallon, we use the same approach as in part (b), finding the z-score for $3.43. Given that the normal distribution is symmetric, the percentage beyond $3.43 is also 50%.
d) Similar to (b), we find the z-score for $3.63 and look up the corresponding percentage, which is approximately 84.13%.
e) The range $3.23 to $3.13 is invalid since $3.23 is greater than $3.13. Therefore, no percentage can be calculated for this range.