Answer to Question #340953 in Statistics and Probability for clah

Question #340953

What is the probability that the 36 tires will have an

average of less than 16,000 miles until the tires begin

to wear out


1
Expert's answer
2022-05-16T17:52:33-0400

We have that: XN(μ,σ2/n)X\sim N(\mu, \sigma^2/n)

μ=16800\mu=16800

σ=3300\sigma=3300

n=36n=36

P(Xˉ<16000)=P(Z<Xμσ/n)P(\bar X<16000)=P(Z<\dfrac{X-\mu}{\sigma/\sqrt{n}})=P(Z<16000168003300/36)=P(Z<1.454545)=P(Z<\dfrac{16000-16800}{3300/\sqrt{36}})=P(Z<-1.454545)

0.0729\approx0.0729


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