Using the z-score table:
Look for the closest area value to 65% in the "Cumulative Area" column of the z-score table. The closest value is 0.6550, which corresponds to a z-score of 0.91.
Using the calculator function:
If your calculator has a norminv function, you can use it to find the z-score corresponding to a cumulative area of 0.6550: norminv(0.6550). This will also give you z = 0.91.
Therefore, the value of z such that 65% of the standard normal curve lies between -z and z is z = 0.91.