A researcher is looking into the effectiveness of a new medicine for the relief of symptoms. He collects random samples of 8 people who are taking the medicine from each of 50 different medical practices. The number of people who say that the medicine is a success, in each sample, is recorded. The results are summarised in the table below. The researcher decides to model this data using a binomial distribution. Show that the mean number of successes per sample is 3.54 (2) He decides to use this mean to calculate expected frequencies. The results are shown in the table below.

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