Find the following probability if z is a standard normal variable: P(z>1.62).
If you mean the probability that the event will occur greater then 1.62 standard deviations from the mean, then
a) you have to use your tables
or b) a computational device or applet (many calculators have these on them).
http://davidmlane.com/hyperstat/z_table.html
To find the probability that a standard normal variable (z) is greater than a given value, such as 1.62, you can use a standard normal distribution table or a calculator.
If you have access to a standard normal distribution table, you need to find the value closest to 1.62 in the table. The table typically provides the area under the curve to the left of a given z-value. However, since we want the probability of z being GREATER than 1.62, we need to find the area to the right of 1.62.
Looking up 1.62 in the table, you might find that the value is not exactly listed. In such cases, you can use the closest listed value and the given area difference to estimate the probability. Take note of the listed value and the corresponding area to the left of that value.
For example, if the table lists 1.61 with an area of 0.9474 and 1.63 with an area of 0.9495, you can estimate that P(z > 1.62) is approximately (1 - 0.9495) = 0.0505.
Keep in mind that this estimated probability is not exact, but it can be a close approximation.
Alternatively, you can use a calculator or statistical software to find the exact probability. Most calculators or software allow you to input the specific value (1.62) and calculate the probability of a standard normal variable being greater than that value directly.