3 (a) The table shows information about the mass of each of 1000 eggs. Mass (m grams) 40 1 m G 50 50 1 m G 56 56 1 m G 64 64 1 m G 70 Frequency 126 520 154 200 (i) Calculate an estimate of the mean. .............................................. g [4] (ii) An egg is picked at random from the 1000 eggs. Find the probability that this egg has a mass greater than 56 g. Give your answer as a fraction in its simplest form. ................................................. [2] (b) One year, a farmer makes a profit of $24 730 selling eggs. Write this profit (i) correct to 2 significant figures $ ................................................ [1] (ii) in standard form. $ ................................................ [1] © UCLES 2023 0580/41/M/J/23 7 (c) On a farm, there are 500 hens, correct to the nearest 10. (i) In one year, the mean number of eggs laid per hen was 320 eggs, correct to the nearest 20. Calculate the upper bound for the total number of eggs all the hens lay in that year. ................................................. [3] (ii) Another farm has 800 hens, correct to the nearest 20. Calculate the lower bound for the difference between the number of hens on the two farms. ................................................. [2] © UCLES 2023 0580/41/M/J/23 [Turn over 8