The lengths of a large stock of titanium rods follow a normal distribution with a mean (𝜇) of 440 mm and a standard deviation (𝜎) of 1 mm

Q. The lengths of a large stock of titanium rods follow a normal distribution with a mean (𝜇) of 440 mm and a standard deviation (𝜎) of 1 mm. What is the percentage of rods whose lengths lie between 438 mm and 441 mm?

            (A) 81.85%           (B) 68.4%                  (C) 99.75%                  (D) 86.64%

Ans: 81.85%

Sol:

Given, mean, (μ) = 440 mm Standard deviation, σ = 1 mm

lower limit,

Percentage of rods whose lengths lie between 438 mm and 441 mm.
= 0.3413 + (0.5 – 0.0228)
= 0.81854 = 81.854%