The national average gas price in 2015 was approximately normally distributed with a mean of \( \$ 2.62 \) and standard deviation of \( \$ 0.35 \). (a) Complete the table with the \( x \)-axis labels on the normal curve. \( \mu-3 \sigma \) \( \mu-2 \sigma \) \( \mu-1 \sigma \) \( \mu+1 \sigma \) \( \mu+2 \sigma \) \( \mu+3 \sigma \) (b) Which graph shows the correctly shaded normal curve to represent gas prices more than \( \$ 3.32 \) ? \( \mu \)

The mean gas price, \( \mu \), is \( \$ 2.62 \), and the standard deviation, \( \sigma \), is \( \$ 0.35 \). To fill out your table with \( x \)-axis labels: - \( \mu - 3\sigma = 2.62 - 3(0.35) = 1.57 \) - \( \mu - 2\sigma = 2.62 - 2(0.35) = 1.92 \) - \( \mu - 1\sigma = 2.62 - 1(0.35) = 2.27 \) - \( \mu + 1\sigma = 2.62 + 1(0.35) = 2.97 \) - \( \mu + 2\sigma = 2.62 + 2(0.35) = 3.32 \) - \( \mu + 3\sigma = 2.62 + 3(0.35) = 3.67 \) For part (b), to represent gas prices more than \( \$ 3.32 \), you would shade the area to the right of \( 3.32 \) on the normal curve, reflecting the tail end of the distribution where those higher prices fall. In history, gas prices have fluctuated dramatically due to various factors such as geopolitical tensions, natural disasters, and shifts in supply and demand. For example, during the 2008 financial crisis, gas prices peaked at around \$4.00 per gallon in the United States. This shows how external factors can create significant ripples in normal distribution for everyday commodities like gas. In real-world applications, analyzing gas price distributions can be useful for businesses in the transport sector and energy markets. By understanding price volatility and trends, companies can better strategize fuel purchases, optimize routing for cost-efficiency, and even develop pricing models to pass savings onto consumers during lower price cycles.