Question

Genetic theory predicts that, in the second generation of a cross of sweet pea plants, blossoms will be either red or white, with each plant independently having a 70% chance of producing red blossoms. Out of 20 plants selected at random from the second generation of this cross, let X be the number that have red blossoms. (a) What is the probability distribution of X? [3] (b) Calculate: (i) the mean and standard deviation of X. [3] (ii) P( X < 12) [2] (iii) P( 9 ≤ X ≤ 13) [2] (c) Would it be unusual to find 18 red plants in the sample? Justify your answer.

Answer 1

(a) Here , X has binomial distribution with parameter n=20 and p=0.70

(b)

(i) mean=np=20*0.70=14

standard deviation=

(ii) Now ,

; From binomial probability table

(iii) Now

; From binomial probability table

(c) Now P(X=18 =0.0278 ; From binomial probability table

Here , the probability that the 18 plants in the sample is less than 0.05

Therefore , it is unusual.