3 The frequency table shows the patient outcomes in a study of a new eye treatment. Outcome Great improvement a Copy the table. Slight improvement b Work out the total frequency. Same or worse c Calculate the relative frequencies. Total frequency d A further 300 people received the treatment. How many would you expect to have improved eyesight? Discussion Is your answer to part d likely to be the exact number of people whose eyesight improved? Frequency Relative frequency 75 20 5 4 a In a survey of 200 households, 65 have high-speed broadband. There are 1000 households in the village. How many would you expect to have high-speed broadband? b 40 parents attended a school meeting. 27 said they preferred to have four school terms. 600 parents have children at the school. How many would you expect to prefer four school terms? 5 Real / Reasoning Restaurant owner Maurice recorded the number of seats reserved for each booking during a week. Seats Frequency 2 30 3 10 4 25 5 5 6 10 Relative frequency Key point Relative frequency can be used to estimate the probability of an event happening. Total frequency a Copy and complete the table. b Estimate the probability that the next booking will be for 2 seats. c Maurice says that it is unlikely that a booking will be for less than 4 people. Is he correct? Explain how you know. d The restaurant has approximately 240 bookings each month. How many of these would you expect to be for 4 seats? Q5b hint Find the relative frequency of a booking for 2 seats. 6 Modelling An agricultural research centre counted the bananas in 1000 bunches. Number of bananas Frequency 200–219 120 220–239 160 240–259 200 260–279 230 280–299 170 300–319 120 Relative frequency Key point Probability can be used to model what happens in the future. a Copy the table and calculate the relative frequencies as percentages. b Estimate the probability that a bunch will contain i 300–319 bananas ii at least 260 bananas. c A grower picks 5000 bunches one week. How many of these would you expect to contain at least 260 bananas? Discussion Why might these estimated probabilities not be a good model for next year's crop? Unit 8 Probability 180