In a region of the UK, \(5 \%\) of people have red hair. In a random sample of size \(n\), taken from this region, the expected number of people with red hair is 3
Calculate the value of \(n\).
A random sample of 20 people is taken from this region. Find the probability that
exactly 4 of these people have red hair,
at least 4 of these people have red hair.
Patrick claims that Reddman people have a probability greater than \(5 \%\) of having red hair. In a random sample of 50 Reddman people, 4 of them have red hair.
Stating your hypotheses clearly, test Patrick's claim. Use a \(1 \%\) level of significance.
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