Question

Algorithmic Given that z is a standard normal random variable, find z for each situation (to 2 decimals).

a. The area to the right of z is 0.03.
b. The area to the right of z is 0.045.
c. The area to the right of z is 0.05.
d. The area to the right of z is 0.2.

Answer 1

To determine the z-score for a given area to the right of it under the standard normal curve, one subtracts the area from 1 to find the area to the left and looks this value up in a z-table, uses a calculator's invNorm function, or utilizes statistical software.

Step-by-step explanation:

To find the z-score corresponding to a given area to the right under the standard normal curve, we can use a z-table, a calculator with statistical functions, or statistical software. The z-table lists the area to the left of the z-score, so to find the area to the right, you would subtract the given area from 1 and then find the corresponding z-score.

• For an area to the right of 0.03, the area to the left is 1 - 0.03 = 0.97. Look this up in the z-table to find the z-score.
• For an area to the right of 0.045, the area to the left is 1 - 0.045 = 0.955. This corresponds to a specific z-score in the table.
• For an area to the right of 0.05, we have 1 - 0.05 = 0.95 to the left, for which we can find the z-score.
• For an area to the right of 0.2, subtract to get 1 - 0.2 = 0.8 to the left, and find the associated z-score.

For example, we use the formula invNorm(1 - area to the right, mean, standard deviation) in a calculator. Thus, for a), invNorm(0.97, 0, 1) gives the z-score. Similar steps are taken for the other parts using their respective areas to the right.