find the probability P(z < -0.46) usind standard normal distribution

Question

please show work -thank you

Answer 1

To find this probability we can first find the probability for z<0.46, which is 0.6772. So this means the probability for 0.46 standard deviations above the mean (to the right of the mean (z=0)). To find the probability for z<-0.46 we subtract this from 1 to give us 0.3228. This is the same as the cumulative probability to the left of z=-0.46 because of symmetry.

Another way to calculate this is to use the fact that 0.6772 is 0.1772 standard deviations above the mean (which corresponds to the mean, z=0). For 0.1772 standard deviations below the mean we subtract 0.1772 from 0.5=0.3228.