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 μ = 25.00 mpg and a standard deviation of σ = 1.75 mpg. (a) What is the standard error of X⎯⎯⎯X¯ , the mean from a random sample of 16 fill-ups by one driver? (Round your answer to 4 decimal places.)  Standard error of   X⎯⎯⎯X¯             _______ (b) Within what interval would you expect the sample mean to fall, with 90 percent probability? (Round your answers to 4 decimal places.)  The interval is from _____ to _______

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Asked Sep 19, 2019
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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 μ = 25.00 mpg and a standard deviation of σ = 1.75 mpg.
 
(a) What is the standard error of X⎯⎯⎯X¯ , the mean from a random sample of 16 fill-ups by one driver? (Round your answer to 4 decimal places.)
  
Standard error of   X⎯⎯⎯X¯             _______
 
(b) Within what interval would you expect the sample mean to fall, with 90 percent probability? (Round your answers to 4 decimal places.)
  
The interval is from _____ to _______

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Expert Answer

Step 1

It is given that the mean and standard deviation are 25.00 mpg and 1.75 mpg, respectively. The sample size n is 16.

Step 2

(a)

The standard error is 0.4375 as obtained as follows:

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Vn 1.75 16 0.4375

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Step 3

(b)

It is given that the sample mean fall with ...

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P(-z< Z < z)0.90 P(Z <z)-P(Z-z)=0.90 P(Z <z)-(1-P(Z<z)) = 0.90 2P(Z <z)1.90 P(Z <z) 0.95

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