a. $p(z > +2.00)$\nb. $p(z > -1.00)$\nc. $p(z < +0.50)$\nd. $p(z < +1.75)$

Explanation:

Step1: Recall the properties of the standard - normal distribution

The total area under the standard - normal curve is 1, and the standard - normal distribution is symmetric about (z = 0). We use the standard - normal table (z - table) to find the cumulative probabilities (P(Z\leq z)).

Step2: Solve part a

For (P(Z>2.00)), we know that (P(Z > z)=1 - P(Z\leq z)). From the z - table, (P(Z\leq2.00)=0.9772). So (P(Z > 2.00)=1 - 0.9772 = 0.0228).

Step3: Solve part b

For (P(Z>-1.00)), since (P(Z > z)=1 - P(Z\leq z)), and from the z - table (P(Z\leq - 1.00)=0.1587). So (P(Z>-1.00)=1 - 0.1587 = 0.8413).

Step4: Solve part c

For (P(Z < 0.50)), we directly look up the value in the z - table. From the z - table, (P(Z < 0.50)=0.6915).

Step5: Solve part d

For (P(Z < 1.75)), we directly look up the value in the z - table. From the z - table, (P(Z < 1.75)=0.9599).

Answer:

a. (0.0228) b. (0.8413) c. (0.6915) d. (0.9599)