Discuss the below:
1. Z is N 17. I distributed. Find (a) P( Z < .6); (b) P( Z <= -.03); (c) P( .12 < Z <= 2.14); (d) P( -1.67 <= Z < 1.20)
2. X is N -10.16 distributed. Find (a) P(X> -12); (b) P(-ll < X <= -8); (c) P(IX+ 101<2); (d) P(IX+lll> 1.5)
3. Suppose that the length X of a random bolt produced by machine A is 1.2 em, on the average, with a standard deviation of .3 em. Assuming that the length X is normally distributed, Find (a) P (X < 1.4); (b) P( X > 1.3); (c) P( I X - 1.21 >.2)
4. X is the actual weight of a bag of concrete (labeled "80 pound bag"). Suppose that E(X) = 81 and 6x. =2. Let Y be the average weigth of 10 bags bought: Y=(X + --------- + X ) / 10. (a) What is the distribution ofY assuming that each bag's weight is normally distributed? Find (b) P (Y => 80); (c) P( IY - 81.5 1<1).