Genetic theory predicts that, in the second generation of across of sweet pea plants, flowers will be either red or white,with each plant having a 25% chance of producing red flowers.Flower colours of separate plants are independent. Let X be thenumber of plants with red flowers out of 20 plants selected atrandom from the second generation of this cross. (a) What is theprobability distribution of X? [3] (b) Calculate: (i) the mean andstandard deviation of X. [3] (ii) P( X > 8) [2] (iii) P( 4 ? X ?10) [2] (c) If only 3 of the 20 plants had red flowers, would thisbe an unusual sample? Calculate a probability and use it to justifyyour answer
