In: Statistics and Probability
the highway fuel economy of a 2016 lexus rx 350 fwd 6 cyinder 3.5l automatic 5 speed using premium fuel is a normally distributed random variable with a mean of u=22.0 mpg and a standard deviation of o=1.25 mpg. 1. what is the standard error of x , the mean from a random sample of 25 fill ups by one driver? 2. within what interval would you expect the sample to fall, with 98 percent probability
Solution:
Given:
X ~ Normal
Part a) what is the standard error of x , the mean from a random sample of 25 fill ups by one driver?
n = sample size= 25
Standard Error is given by formula:
Part b) Within what interval would you expect the sample to fall, with 98 percent probability ?
That is find sample mean values in which all sample mean fall with 98% probability.
First find z values such that:
P( -z < Z < z) = 0.98
Area between -z and +z is 0.98 then total area below +z is:
Area = ( 1 + 0.98) /2 = 1.98 / 2 = 0.9900
Thus look in z table for Area = 0.9900 or its closest area and find corresponding z critical value.
Area 0.9901 is closest to 0.9900 , thus corresponding z value is 2.3 and 0.03
Thus z = 2.33
Thus use following formula to find and
and
Thus within 21.42 and 22.58 we would expect the sample to fall, with 98 percent probability.