Question

Question 2

Ms Greenaway sells mangoes at a roundabout in her town. On any given day, the probability of Ms Greenaway selling 0 mangoes is 0.1, the probability of Ms Greenaway selling 1 mango is 0.7 and the probability of Ms Greenaway selling 2 mangoes is 0.2.

(a) Construct the probability distribution table for Ms Greenaway’s mango sales. [3 mark]

(b) Calculate Ms Greenaway’s expected daily mango sales and the standard deviation of Ms Greenaway’s daily mango sales.

Answer 1

Let X = the number of mangoes sale by the Ms Greenaway

From the given information X takes values as 0, 1, 2 with probabilities 0.1, 0.7 and 0.2 respectively.

So the the probability distribution table for Ms Greenaway’s mango sales is as follow:

X	P(X =x)
0	0.1
1	0.7
2	0.2
Total	1

b) The formula of expected value of X is

So, E(X) = 0*0.1 + 1*0.7 + 2 * 0.2 = 0.7 + 0.4 = 1.1 mangoes.

The formula of standard deviation is as

E(X² ) = 0² *0.1 + 1²​​​​​​​ *0.7 + 2²​​​​​​​ *0.2 = 0+ 0.7 + 0.8 = 1.5

So that the standard deviation of X is