Q7 (RV25) [Maximum mark: 10] John decided to build a stone fence around his house and lay a stone walkway. John ordered a large bag of stones and first chose a random a sample of 50 stones for measuring. He measured the diameters of the stones correct to the nearest centimetre. The following table shows the frequency distribution of these diameters. Diameter, cm Frequency 14 6 15 11 16 20 17 9 18 (a) Find the value of (i) the mean diameter of these stones; (ii) the standard deviation of the diameters of these stones. [2] John assumes that the diameters of all the stones from this bag are normally distributed with a mean 16 em and a standard deviation of 1.1 cm. John sorts all stones by their diameter size.(b) John selects the largest stones, with diameters of 18 cm or greater, to use for the stone walkway. Estimate the percentage of stones used. (c) John selects small stones, which have a diameter less than a cm to use for a walkway border. The small stones account for 5% of the total number of stones. Calculate the value of r. [2) (d) John selects medium stones to use the stone fence. Estimate the percentage of medium stones with diameter more than a cm from part (c) and less than 18 cm. (e) John estimates that there are about 10 000 stones in total. Estimate the number of large stones. [2]