Final answer:
To find P(z ≤ -1.65), use the z-table to locate the corresponding area under the curve. For P(x > 65), convert the x-value to a z-score, then find the area to the left of the z-score on the z-table and subtract from 1. Use invNorm to find specific critical values on a calculator or computer.
Step-by-step explanation:
To calculate P(z ≤ -1.65), you refer to the z-table, which provides the area under the normal curve to the left of a given z-score. You would find the row in the z-table corresponding to -1.6 and then the column corresponding to 0.05 (since the second decimal of -1.65 is 5), and at the intersection, you will find the area to the left of -1.65.
To find P(x > 65), you would first need to convert the x-value to a z-score if you are working with a normal distribution. This involves using the mean (μ) and standard deviation (σ) of the distribution and the formula z = (x - μ) / σ. Once you have the z-score, you can use the z-table to find the area to the left of the z-score and subtract it from 1 to get the area to the right. This gives you P(x > 65).
In case of finding a specific critical value, like z0.01, which leaves an area of 0.01 to the right, you can use the invNorm function on a calculator like the TI-83 or using a computer program, where you would enter invNorm(0.99,0,1) to find the z-score that has 0.99 area to the left of it.