The lifetimes of Econ light bulbs are normally distributed with mean 1000 h and standard deviation 25 h.

(a) Find, to three decimal places, the probability that an Econ light bulb will have a lifetime between 975 h and 1020 h.

(b) Calculate, to three decimal places, the probability that the sum of the lifetimes of eight Econ light bulbs will exceed 7930 h. Indicate clearly the stage in your calculation when an assumption concerning independence is essential. The lifetimes of Enersaver light bulbs are normally distributed with mean 7900 h and standard deviation 50 h.

(c) Calculate, to three decimal places, the probability that an Enersaver light bulb will last at least eight times as long as an Econ light bulb. (NEAB)