Question

In: Statistics and Probability

The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using...

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 = 22.00 mpg and a standard deviation of σ = 1.25 mpg.

(a) 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.)
  
Standard error of x = _______

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

The interval is from __________ to ___________

Solutions

Expert Solution

Solution :

Given that,

mean = = 22.00 mpg

standard deviation = = 1.25 mpg

n = 25

a) = = 22.00

= / n = 1.25 / 25 = 0.25

b)  Using standard normal table,

P( -z < Z < z) = 98%

= P(Z < z) - P(Z <-z ) = 0.98

= 2P(Z < z) - 1 = 0.98

= 2P(Z < z) = 1 + 0.98

= P(Z < z) = 1.98 / 2

= P(Z < z) = 0.99

= P(Z < 2.33) = 0.99

= z  ± 2.33

Using z-score formula,

= z * +

= -2.33 * 0.25 + 22.00

= 21.4175

Using z-score formula,

= z * +

= 2.33 * 0.25 + 22.00

= 22.5825

The interval is from 21.4175 to 22.5825


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