Step 1

Standard Normal Distribution is symmetric continuous distribution with mean 0 and variance 1.

-The mean is located at the center of the distribution.

This is True because here the center of the distribution is 0 and the mean is also 0.

-The total area under the curve is equal to 1.00.

This is True because area under curve of any distribution will be always 1

-The curve is continuous.

This is True because it takes values on continuous domain

-The mean is 0 and the standard deviation is 1.

This is True by the definition of Standard Normal Distribution.

Step 2

b. \(P(Z< -0.51) = \Phi(-0.51) = 0.305026 [ \text{From the table of Standard Normal Distribution} , \Phi\ \text{is the CDF of Standard Normal Distribution} ]\)

c. \(P(z > - 0.59) = 1 - \Phi(-0.59) = 1 - 0.277595 = 0.722405 [ \text{From the table of Standard Normal Distribution} , \Phi\ \text{is the CDF of Standard Normal Distribution} ]\)