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June 2018 p62 q7
3299
In a certain country, 60% of mobile phones sold are made by Company A, 35% are made by Company B and 5% are made by other companies.
Use a suitable approximation to find the probability that, out of a random sample of 130 people who buy a mobile phone, at least 50 choose a mobile phone made by Company B.
Solution
Let the random variable \(X\) represent the number of people who choose a mobile phone made by Company B. \(X\) follows a binomial distribution with parameters \(n = 130\) and \(p = 0.35\).
We approximate this binomial distribution with a normal distribution. The mean \(\mu\) and variance \(\sigma^2\) of the binomial distribution are given by: