1. Find the following areas under the standard normal curve. Round answers to places.
a) the area to the left of $z=0.64$.
b) the area to the right of $\mathrm{z}=1.23$.
c) the area that lies between -1.02 and 0.89 .
d) the area that lies outside the interval from $z=-0.73$ to $z=1.55$

Step 1 ：Given the z-values, we need to find the corresponding areas under the standard normal curve.

Step 2 ：For part a), we need to find the area to the left of z=0.64. This is equivalent to finding the cumulative distribution function (CDF) at z=0.64. Using the standard normal distribution table or a calculator, we find that the area to the left of z=0.64 is approximately 0.739.

Step 3 ：For part b), we need to find the area to the right of z=1.23. This is equivalent to finding 1 minus the cumulative distribution function (CDF) at z=1.23. Using the standard normal distribution table or a calculator, we find that the area to the right of z=1.23 is approximately 0.109.

Step 4 ：For part c), we need to find the area that lies between -1.02 and 0.89. This is equivalent to finding the difference between the cumulative distribution function (CDF) at z=0.89 and the cumulative distribution function (CDF) at z=-1.02. Using the standard normal distribution table or a calculator, we find that the area that lies between -1.02 and 0.89 is approximately 0.659.

Step 5 ：For part d), we need to find the area that lies outside the interval from z=-0.73 to z=1.55. This is equivalent to finding 1 minus the difference between the cumulative distribution function (CDF) at z=1.55 and the cumulative distribution function (CDF) at z=-0.73. Using the standard normal distribution table or a calculator, we find that the area that lies outside the interval from z=-0.73 to z=1.55 is approximately 0.293.

Step 6 ：Final Answer: \(\boxed{a) 0.739, b) 0.109, c) 0.659, d) 0.293}\)