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(b) An assembly line contains 2000 components with a limited lifespan. Records show that the life span of the components is normally distributed with a mean life of 900 hours and a standard deviation of 80 hours.

(i) What proportion of components will fail before 1000 hours?

(ii) What proportion will fail before 750 hours?

(iii) What proportion will fail between 820 hours and 980 hours?

(iv) From the sample above of 100 components, the mean length of the components was calculated as 5.2 m with a standard deviation of 2 m. Find the 95% confidence interval for the mean length of all components.