Answer to Question #340953 in Statistics and Probability for clah

Question

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

Answer 1

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

$\mu=16800$

$\sigma=3300$

$n=36$

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

$$\approx0.0729$$