The gas prices in 2017 were normally distributed with a mean of \( \$ 2.99 \) and a standard deviation of \( \$ 0.19 \) You may find it helpful to use the Normal Distribution tool. (a) Find the probability for a gas price less than \( \$ 3.43 \). Enter a percent rounded to two decimal places. Include the \( \% \) symbol in your answer. i.e. \( 1234=12.34 \% \). The probability is (b) Find the gas price in the 75 th percentile (use the Find Percentile tab of the stats tool). Please round your answer to two decimal places. \( \$ \)

To find the probability of a gas price less than \( \$ 3.43 \), you would use the Z-score formula: \[ Z = \frac{X - \mu}{\sigma} \] where \( X = 3.43 \), \( \mu = 2.99 \), and \( \sigma = 0.19 \). Plugging in the values, \[ Z = \frac{3.43 - 2.99}{0.19} \approx 2.32 \] Using the standard normal distribution table, or a calculator, you can find that the cumulative probability for \( Z = 2.32 \) is approximately 0.9898. So, the probability for a gas price less than \( \$ 3.43 \) is about \( 98.98\% \). For part (b), to find the 75th percentile gas price, you would look for the Z-score that corresponds to 0.75 in the standard normal distribution, which is approximately \( 0.674 \). Now, using the formula \( X = \mu + Z\sigma \): \[ X = 2.99 + 0.674 \cdot 0.19 \approx 3.09 \] Therefore, the gas price in the 75th percentile is approximately \( \$ 3.09 \).