A metallic split ring has a target internal diameter of 50 mm, but records show that the diameters are normally distributed with mean 50 mm and standard deviation 0.07 mm. An acceptable diameter is one within the range 49.93 mm to 50.07 mm. What proportion of the output is unacceptable?

Step-by-step explanation:

Mass-produced items should conform to a specification. Usually, a mean is aimed for but due to

random errors in the production process a tolerance is set on deviations from the mean. For example

if we produce piston rings which have a target mean internal diameter of 45 mm then realistically

we expect the diameter to deviate only slightly from this value. The deviations from the mean value

are often modelled very well by the normal distribution. Suppose we decide that diameters in the

range 44.95 mm to 45.05 mm are acceptable, then what proportion of the output is satisfactory? In

this Section we shall see how to use the normal distribution to answer questions like this.

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).