The distribution of the diameters of ball bearings made under a given manufacturing process is normally distributed with a mean of 4 cm and a standard deviation of 0.2 cm. what proportion of the ball bearings will have a diameter less than 3.7 cm?
Given that the bearings are normally distributed with mean of 4 cm and standard deviation of 0.2 cm, then to evaluate the proportion of of the bearings that have the diameter of less than 3.7 cm we proceed as follows: P(x<3.7)=P(z<Z) Z=(x-μ)/σ where: μ=4 cm σ=0.2 cm thus Z=(4-3.7)/0.2 Z=0.15 Hence: P(z<0.15)=0.5596 hence the answer is 55.96%
