The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of u = 26.75 mpg and a standard deviation of o = 3.50 mpg. (a) What is the standard error of X , the mean from a random sample of 36 fill-ups by one driver? (Round your answer to 4 decimal places.) Standard error of X (b) Within what interval would you expect the sample mean to fall, with 99 percent probability? (Round your answers to 4 decimal places.) The interval is from to < Prey 3 of 10 Next > 46°F Rain showers to search 近

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### Problem Context:
The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of \(\mu = 26.75\) mpg and a standard deviation of \(\sigma = 3.50\) mpg.

#### Questions:

**(a)** What is the standard error of \(\overline{X}\), the mean from a random sample of 36 fill-ups by one driver? (Round your answer to 4 decimal places.)

- **Standard error of \(\overline{X}\):** [ ]

**(b)** Within what interval would you expect the sample mean to fall, with 99 percent probability? (Round your answers to 4 decimal places.)

- **The interval is from [ ] to [ ]**
Transcribed Image Text:### Problem Context: The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of \(\mu = 26.75\) mpg and a standard deviation of \(\sigma = 3.50\) mpg. #### Questions: **(a)** What is the standard error of \(\overline{X}\), the mean from a random sample of 36 fill-ups by one driver? (Round your answer to 4 decimal places.) - **Standard error of \(\overline{X}\):** [ ] **(b)** Within what interval would you expect the sample mean to fall, with 99 percent probability? (Round your answers to 4 decimal places.) - **The interval is from [ ] to [ ]**
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