Question

Finding the probabilities using standard normal distribution 1) P(0 < z < 1.96)  2) P(0 < z < 0.67)
 please show work / formulas

Answer 1

When z=0 this corresponds to 0.5 or 50%, the central division of the symmetrical normal distribution. There is an equal probability of being on the left or right side of this division (the mean), half on the left and half on the right.

1. z=1.96 corresponds to 0.9750 or 97.5%. The probability is therefore 97.5-50=47.5%.
2. z=0.67 corresponds to 0.7486 or 74.86%. So the probability is 74.86-50=24.86%.