Calculate P(15.99 ≤ X ≤ 16.01) when n = 16.

Question

The inside diameter of a randomly selected piston ring is a random variable with mean value 16 cm and standard deviation 0.05 cm. Suppose the distribution of the diameter is normal. (Round your answers to four decimal places.)

 

Answer 1

The Z score for the limits is Z(15.99)=(15.99-16)/0.05=-0.2; Z(16.01-16)/0.05=0.2.

P(0.2)=0.5793, P(-0.02)=1-P(0.2)=0.4207. Therefore P(0.2)-P(-0.2)=2P(0.2)-1=1.1586-1=0.1586.

The probability of the inside diameter being between 15.99 and 16.01 cm is 0.1586 or 15.86%.