You measure the lifetime of a random sample of 64 tires of a certain brand. Suppose that the lifetimes for tires of this brand follow a normal distribution, with unknown mean μ and standard deviation σ = 5 kg. What is the 99% confidence interval?

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Answer 1 · 2017-04-07T06:45:56

Population mean lies in between $mu=barx+1.6125$ and $mu=barx-1.6125$

let the Sample mean be $=x$
Sample Standard Deviation $sigma = 5 kg$
Sample size $n=64$

Then -

Standard Error $SE=sigma/sqrtn=5/sqrt64=5/8=0.625$

Population Mean

$mu=barx+-(zxxSE)$
$mu=barx+-(2.58xx0.625)$
$mu=barx+-1.6125$

Population mean lies in between $mu=barx+1.6125$ and $mu=barx-1.6125$

Look at the diagram