Final answer:
To find these probabilities for the standard normal distribution, use a z-table, calculator, or software. Look up the corresponding z-scores in the table: z < 1.2, 1 - the area to the left of z=0.7, and the difference between the areas to the left of z=1.3 and z=-0.2.
Step-by-step explanation:
To calculate the probabilities for a normal distribution, one would typically use a z-table, a calculator, or statistical software that provides the area under the normal curve, which represents probabilities associated with each z-score. Here's how you can determine each of the three probabilities mentioned in the question:
P (z < 1.2): To find this probability, look up 1.2 in the z-table, which will give you the area under the curve to the left of z=1.2.
P (z > 0.7): To find this probability, first look up 0.7 in the z-table to get the area to the left of z=0.7, then subtract this value from 1 to get the area to the right of z=0.7.
P (–0.2 < z < 1.3): To find the probability that z is between -0.2 and 1.3, find the areas to the left of z=1.3 and z=-0.2 and subtract the smaller area from the larger area.
Remember that a z-score represents how many standard deviations an element is from the mean of the distribution. The standard normal distribution has a mean of 0 and a standard deviation of 1, which simplifies the process of calculating these probabilities.