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 $μ = ¯ x + 1.6125$ $mu=barx+1.6125$ and $μ = ¯ x - 1.6125$ $mu=barx-1.6125$

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

Then -

Standard Error $S E = \frac{σ}{\sqrt{n}} = \frac{5}{\sqrt{64}} = \frac{5}{8} = 0.625$ $SE=sigma/sqrtn=5/sqrt64=5/8=0.625$

Population Mean

$μ = ¯ x \pm (z \times S E)$ $mu=barx+-(zxxSE)$
$μ = ¯ x \pm (2.58 \times 0.625)$ $mu=barx+-(2.58xx0.625)$
$μ = ¯ x \pm 1.6125$ $mu=barx+-1.6125$

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

Look at the diagram