Ball bearings are manufactured with a mean diameter of 5 millimeters (mm). Because of variability in the manufacturing process, the diameters of the ball bearing are approximately normally distributed, with a standard deviation of 0.02 mm. A ball bearings that have a diameter less than 4.95 mm or greater than 5.05 mm are discarded. What proportion of ball bearings will be discarded? Show your work
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Let us define the random variable X as the diameter of Ball bearings follows Normal distribution with mean millimeters and standard deviation mm.
Given that the Ball bearings are considered as discarded if the diameter less than 4.95 mm or greater than 5.05 mm.
That is, the Ball bearings are considered as discarded if .
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
