A random variable X is Normally distributed with mean -5.5}) ? A) 0.233 B) 0.512 C) 0.767 D) 0.488 E) Not within ± 0.005 of any of the above class=answers-bank-image d-inline rel=preload = 75 and -5.5}) ? A) 0.233 B) 0.512 C) 0.767 D) 0.488 E) Not within ± 0.005 of any of the above class=answers-bank-image d-inline rel=preload = 8.Let Y be a second Normally distributed random variable with mean -5.5}) ? A) 0.233 B) 0.512 C) 0.767 D) 0.488 E) Not within ± 0.005 of any of the above class=answers-bank-image d-inline rel=preload = 70 and -5.5}) ? A) 0.233 B) 0.512 C) 0.767 D) 0.488 E) Not within ± 0.005 of any of the above class=answers-bank-image d-inline rel=preload = 12.It is also known that X and Y are independent of one another.Let W be a random variable that is the difference between X and Y (i.e. ,W = X - Y) .What is the probability that W is greater than -5.5 (i.e. ,P{W -5.5}) ?A) 0.233B) 0.512C) 0.767D) 0.488E) Not within ± 0.005 of any of the above

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A random variable X is Normally distributed with mean   -5.5}) ? A) 0.233 B) 0.512 C) 0.767 D) 0.488 E) Not within ± 0.005 of any of the above class=answers-bank-image d-inline rel=preload > = 75 and   -5.5}) ? A) 0.233 B) 0.512 C) 0.767 D) 0.488 E) Not within ± 0.005 of any of the above class=answers-bank-image d-inline rel=preload > = 8.Let Y be a second Normally distributed random variable with mean   -5.5}) ? A) 0.233 B) 0.512 C) 0.767 D) 0.488 E) Not within ± 0.005 of any of the above class=answers-bank-image d-inline rel=preload > = 70 and   -5.5}) ? A) 0.233 B) 0.512 C) 0.767 D) 0.488 E) Not within ± 0.005 of any of the above class=answers-bank-image d-inline rel=preload > = 12.It is also known that X and Y are independent of one another.Let W be a random variable that is the difference between X and Y (i.e. ,W = X - Y) .What is the probability that W is greater than -5.5 (i.e. ,P{W > -5.5}) ?A) 0.233B) 0.512C) 0.767D) 0.488E) Not within ± 0.005 of any of the above

Maddie Sirko · Accepted Answer

Final Answer : C, Explanation :  The mean of W is (the mean of X) - (the mean of Y) = 75 - 70 = 5.The variance of W is (the variance of X) + (the variance of Y) = 8^2 + 12^2 = 208.Therefore, W ~ N(5, 208).To find P{W > -5.5}, we first standardize:P{W > -5.5} = P{(W - 5)/sqrt(208) > (-5.5 - 5)/sqrt(208)} = P{Z > -0.479}= 1 - P{Z <= -0.479} = 1 - 0.317 (from standard normal table) = 0.683.Therefore, the answer is C.

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