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mnphys
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Homework Statement
A random sample of 100 automobile owners in the state of Virginia shows that an automobile is driven on average 23,500 kilometers per year with a standard deviation of 3900 kilometers. Assume the distribution of the measurements to be approximately normal. Construct a 99% prediction interval for the kilometers traveled annually by an automobile owner in Virginia.
Homework Equations
x-bar is the mean, z-value is self-explanatory, σ is the standard deviation and n is the sample size.
The Attempt at a Solution
Here is my attempt at a solution:
However, the book has the bounds as (13,075, 33,925).
I also considered trying a t-value instead of z-value, but...
a) the book uses z-values for problems like this
b) the book never, ever asks for a t-value with n > 30
c) the t-value I do get if I try it that way doesn't work anyway.
I did this backwards based on the book's answer. With an interval of 10425, standard deviation of 3900, and n=100, the z/t value you would need is 2.66 - this doesn't work as a z-value, and as a t-value it would only work with a sample size of 60 or so. Please help, I'm lost!