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Given a random variable XX following normal distribution with mean of -3 and standard deviation of...

Given a random variable XX following normal distribution with mean of -3 and standard deviation of 4. Then random variable Y=0.4X+5Y=0.4X+5 is also normal.

(1)(2pts) Find the distribution of YY, i.e. μY,σY.μY,σY.

(2)(3pts) Find the probabilities P(−4<X<0),P(−1<Y<0).P(−4<X<0),P(−1<Y<0).

(3)(3pts) Find the probabilities P(−4<X¯<0),P(3<Y¯<4).P(−4<X¯<0),P(3<Y¯<4).

(4)(4pts) Find the 53th percentile of the distribution of XX.

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