Please show work x has a normal distribution with mu40 and 2

Please show work!

x has a normal distribution with mu=40 and ?²= 36. Find value of x, call it x0, such that:

Solution

a) P(x>= x0) =0.1

=> P(x<= x0) = 1-0.1 =0.9

0.9 corresponds to z value = 1.28

Therefore,

1.28 = ( x0 - 40) /6

=> x0 = 47.68 Answer

b) P(x<x0) =0.05

0.05 corresponds to z value = -1.65

Therefore,

-1.65 = ( x0 - 40) /6

=> x0 = 40 - 9.90 = 30.1 Answer

c) P(x>= x0) =0.4

=> P(x<= x0) = 1-0.4 =0.6

0.6 corresponds to z value = 0.26

Therefore,

0.26 = ( x0 - 40) /6

=> x0 = 41.56 Answer