Suppose the random variablesX1,2, and, As are mutually independent and represent

Question

Suppose the random variablesX1,2, and, As are mutually independent and represent the time it takes to gather ingredients, prepare/cook the ingredients, and assemble the ingredients, respectively. The total meal preparation time is thus Y-Xi + X2 + Xz. Xi is normally distributed with mean 12 and standard deviation 2. X2 is normally distributed with mean 14 and standard deviation 2. X is normally distributed with mean 6 and standard deviation 1. a. What is the distribution of Y? O multinomial O geometric O normal negative multinomial Poisson O multivariate normal O exponential Submit Answer Tries 0/10 Round all answers to 4 decimal points. b. Find E(Y) Submit Answer Tries 0/5 c. Find Var( XX2 Submit Answer Tries 0/5 d. Find Var(Y). Submit Answer Tries 0/s e. Find P(Y 26) Submit Answer Tries 0/5

Explanation / Answer

a. is normally sitributed

b . E(Y) = 12+14+6 = 32

c.Var(X1+X2) = 2^2 +2^2 = 8

d.Var(X1+X2+X3) = 2^2 +2^2+1 = 9

e. P(Y<35 ) = 0.6306

f. P(Y>26) = 0.7475

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