Question

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 = 20.00 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 36 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 99 percent probability? (Round your answers to 4 decimal places.)
  
The interval is from  to

Answer 1

Solution :

Given that,

mean = = 20

standard deviation = = 2

n = 36

(a)

= 20

The sampling distribution of standard deviation is ,  

= / n = 2 / 36 = 2 / 6 = 0.3333

Using Empirical rule,

P(  - 3 < X <   + 3 ) = 99%

P(20 - 3 * 0.3333 < X < 20 + 3 * 0.3333) = 99%

P(19 < X < 21) = 99%

Interval : 19 to 21