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 X.