stastitics in qualitative and quantitative geography

Question

The target internal diameter of producing a car tyre is 45mm but records shows that the tyres are normally distributed with the mean of 45mm and standard deviation of 0.05mm. An acceptable diameter is within the range of 44.95mm to 45.05mm. What proportion is unacceptable?

Answer 1

μ = 45 mm, σ = 0.05 mm

X → N(45, 0.05)

X-45/0.05 → N (0, 1)

Given that 44.95 ≤ x ≤ 45.5

-0.05/0.05 ≤ x-45/0.05 ≤ 0.05/0.05

-1 ≤ X ≤ 1  (Let X = x-45/0.05)

P(-1 ≤ X ≤ 1) = 2(0.8413 - 0.5)

= 2 x 0.3413

= 0.6826