(b) If an output component is only accepted when its length lies in the range between 112.8 mm and 168.0 mm , find
the expected proportion of components that are accepted. i.e. determine the below probability. Enter your answer
rounded correct to 4 decimal places
Number mm

To find the expected proportion of components accepted within the length range of 112.8 mm to 168.0 mm, we can use the properties of a normal distribution, assuming that the lengths are normally distributed. First, we need the mean (μ) and standard deviation (σ) of the distribution to calculate the probabilities using the cumulative distribution function (CDF).

Suppose the lengths are normally distributed with mean μ and standard deviation σ. We would transform the lengths into z-scores:

Without specific values for μ and σ, I can’t provide an exact numerical answer. However, once you calculate it with your specific values, remember to round it to 4 decimal places.