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June 2015 p63 q3
3314
On a production line making cameras, the probability of a randomly chosen camera being substandard is 0.072. A random sample of 300 cameras is checked. Find the probability that there are fewer than 18 cameras which are substandard.
Solution
Let the random variable \(X\) represent the number of substandard cameras in a sample of 300. \(X\) follows a binomial distribution with parameters \(n = 300\) and \(p = 0.072\).
We approximate this binomial distribution with a normal distribution, where the mean \(\mu\) and variance \(\sigma^2\) are given by: