The combined city/highway fuel economy of a 2023 Lexus UX 250 Hybrid is a normally distributed random variable with a mean of \( \mu= \) 22.00 mpg and a standard deviation of \( \sigma=1.25 \mathrm{mpg} \). (a) What is the standard error of \( \bar{X} \), the mean from a random sample of 25 fill-ups by one driver? Note: Round your answer to 4 decimal places. Standard error of \( \bar{X} \)

To calculate the standard error (SE) of \( \bar{X} \), you use the formula: \[ SE = \frac{\sigma}{\sqrt{n}} \] where \( \sigma \) is the standard deviation and \( n \) is the sample size. For the 2023 Lexus UX 250 Hybrid, \( \sigma = 1.25 \) mpg and \( n = 25 \). Now plugging in the values: \[ SE = \frac{1.25}{\sqrt{25}} = \frac{1.25}{5} = 0.25 \] So, the standard error of \( \bar{X} \) is **0.2500 mpg** when rounded to four decimal places.