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 = 25.25 mpg and a standard deviation of σ = 2.00 mpg. (a) What is the standard error of X⎯⎯⎯X¯ , the mean from a random sample of 9 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 95 percent probability? (Round your answers to 4 decimal places.)  The interval is from ________ to _________

Question
Asked Sep 29, 2019
30 views

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 = 25.25 mpg and a standard deviation of σ = 2.00 mpg.
 
(a) What is the standard error of X⎯⎯⎯X¯ , the mean from a random sample of 9 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 95 percent probability? (Round your answers to 4 decimal places.)
  
The interval is from ________ to _________

check_circle

Expert Answer

Step 1

Note: X- (X-bar) is considered as X-bar.

a.Finding the standard error of X-bar, the mean from a random sample of 9 fill-ups by one driver:

The standard error of X-bar is σ/sqrt(n).

The standard deviation, σ = 2.00 and n = 9.

Thus, the standard error of X-bar, the mean from a random sample of 9 fill-ups by one driver is, σ/sqrt(n) = 2/sqrt(9) = 0.6667.

Step 2

b. finding the interval within which the sample mean will fall with 95% probability:

A 95% confidence interval for the true mean is as follows:

х -t, x SE <и <х+t,x SE
2
help_outline

Image Transcriptionclose

х -t, x SE <и <х+t,x SE 2

fullscreen
Step 3

It is given that, X-bar = 25.25 and n = 9.

The degrees of freedom is, n-1 = 9-1 =8.

For a 95% confidence level, the value of tα/2  calculated usi...

x SE <u <x +t x SE
3-
C
2
2
25.25-2.306 (0.6667) < i < 25.25 + 2.306 (0.6667)
23.71 u26.78
help_outline

Image Transcriptionclose

x SE <u <x +t x SE 3- C 2 2 25.25-2.306 (0.6667) < i < 25.25 + 2.306 (0.6667) 23.71 u26.78

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Other

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: A random sample of 28 lunch orders at Noodles &amp; Company showed a standard deviation of $6.24. Fi...

A: Confidence interval:The (1-α) % confidence interval for population standard deviation is given by:

question_answer

Q: A random sample of 10 shipments of stick-on labels showed the following order sizes.  36,575 30,1...

A: Solution:First we need to find the mean and standard deviation of the given data. 

question_answer

Q: A quantitative data set of size 80 has mean 35 and standard deviation 33. At least how many observat...

A: It is given that the mean and standard deviation of the quantitate data set are 35 and 33, respectiv...

question_answer

Q: The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of ...

A: (a) The probability that at least 66 flights arrive on time. From the given information, the percent...

question_answer

Q: Two professors are applying for grants. Professor Jane has a probability of 0.66 of being funded. Pr...

A: It is given that probability of Jane funded is 0.66 and probability of Joe funded is 0.29.

question_answer

Q: Suppose a car driven under specific conditions gets a mean gas mileage of 40 miles per gallon with a...

A: Assuming that the mileage data is normally distributed, we'll calculate the z-statisic and then find...

question_answer

Q: Help me solve it with explanation

A: To find relative frequency, frequency for each interval is divided by total number of data values.To...

question_answer

Q: Consider the following data:Monthly Profit of an Auto Repair Shop Month Jan-14 Feb-14 Mar-14 Apr-...

A: The exponential smoothing forecast for the next time period (Oct-14) is 19,193.2 and it is calculate...

question_answer

Q: How can you find the conditional distribution?

A: Conditional distribution:The conditional probability is defined as the probability distribution for ...