The random variable Z has a standard normal distribution Fin

The random variable Z has a standard normal distribution.

Find z

P( Z <_ z) = 0.82

P( Z >_ z) = 0.59

P(-z <_ Z <_ z)= 0.65

Find z_0.15

Solution

P( Z <_ z) = 0.82

So z=0.92 (from standard normal table)

-----------------------------------------------------------------------------------

P( Z >_ z) = 0.59

So z= -0.23 (from standard normal table)

-----------------------------------------------------------------------------------

P(-z <_ Z <_ z)= 0.65

So z= 0.93(from standard normal table)

-----------------------------------------------------------------------------------

Find z_0.15

So z= -1.04(from standard normal table)