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a. P(18) = 0.25

b. P(X > 18) = P(X=20) + P(X=24) + P(X=27)

= 0.2 + 0.17 + 0.16 = 0.53

c. P(X<=18) = P(X=18) + P(X=13) = 0.25 + 0.22 = 0.47

d. Mean of X = (13+18+20+24+27)/5 = 102/5 = 20.4

e. Variance of X = sigma^2 = sum(Xi-mean)^2/N =

( (13-20.4)^2 + (18-20.4)^2 + (20-20.4)^2 + (24-20.4)^2 + (27-20.4)^2) / 5

Solving this for sigma^2, you get 29.3

Therefore, variance = 29.3

f. Standard deviation = sigma = (29.3)^0.5 = 5.4129

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