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The normal approximation to the binomial distribution

The normal approximation to the binomial distribution problem 3

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A large number of runners took part in two charity runs to raise money for a new community centre. In the first run, the times to complete the run were normally distributed with mean 46.3 seconds and standard deviation 6.4 seconds. 150 runners are chosen at random from those who took part in the second run. Use an approximation to find the probability that fewer than 20 of the 150 runners took more than 48.6 seconds to complete the run.

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