Probability and proportion from standard deviation and mean

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  1. The lifetimes of a colour TV picture tube is normally distributed, with a mean of 8 yrs and a standard deviation of 2 years.

(i) What is the probability that a picture tube will last more than 10 yrs?

(ii) If the firm guarantees the picture tube for 4 yrs, what percentage of the tubes sold will have to be replaced?

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Hint: for i, you need the lifetime to be more than one standard deviation high. for ii, it needs to be more than 2 standard deviations low.