The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 35 L

The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 3.5 L automatic 5?speed using premium fuel is a normally distributed random variable with a mean of ? = 22 MPG and a standard deviation of ? = 1.25 MPG.

Within what interval would you expect the sample mean to fall, with 98 percent probability? (Round your answers to 4 decimal places.)

The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 3.5 L automatic 5?speed using premium fuel is a normally distributed random variable with a mean of ? = 22 MPG and a standard deviation of ? = 1.25 MPG.

The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 3.5 L automatic 5?speed using premium fuel is a normally distributed random variable with a mean of ? = 22 MPG and a standard deviation of ? = 1.25 MPG. What is the standard error of X , the mean from a random sample of 25 fill?ups by one driver? (Round your answer to 4 decimal places.) Within what interval would you expect the sample mean to fall, with 98 percent probability? (Round your answers to 4 decimal places.)

Solution

(a)the standard error =s/vn

=1.25/sqrt(25)

=0.25

-----------------------------------------------------------------------------------------------------------

(b) Given a=1-0.98=0.02, Z(0.01)=2.33 (from standard normal table)

So the lower bound is

xbar - Z*s/vn=22 - 2.33*0.25 = 21.4175

So the upper bound is

xbar + Z*s/vn =22 + 2.33*0.25=22.5825