SOLUTION: 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 = 25.50 mpg an

Algebra ->  Probability-and-statistics -> SOLUTION: 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 = 25.50 mpg an      Log On


   

Question 1200576: 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 = 25.50 mpg and a standard deviation of σ = 2.25 mpg.

(b) Within what interval would you expect the sample mean to fall, with 98 percent probability? (Round your answers to 4 decimal places.)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mean is 25.5 mpg
standard deviation is 2.25 mpg
critical z-score for 98% probability = plus or minus z = 2.326347877.
z = (x - m) / s
z is the z-score
x is the raw score
m is the poulation mean
s is the population standard deviation
to solve for x, the formula becomes:
x = z * s + m
when z = 2.326347877 and m = 25.5 and s = 2.25, the formula becomes:
x = -2.326347877 * 2.25 + 25.5 = 20.26571728 on the low side.
x = 2.326347877 * 2.25 + 25.5 = 30.734202672 on the high side.
rounds as required.
this is what it looks like, using the calculator at https://davidmlane.com/hyperstat/z_table.html