EXAMPLE 34Find the -value with given area to its right

Find the standard normal -value that has area 0.03 to the right of it.

Solution

  • Step 1 Draw the standard normal curve. Label the . Shade the area to the right of it with the given area, as shown in Figure 39.

  • Step 2 The table contains areas to the left of values of , so we must find the area to the left of the specific value , as follows:

    So the area to the left of is .

    image
    Figure 6.41: FIGURE 39 has an area 0.03 to the right of it.
  • Step 3 Look up 0.97 on the inside of the table. The closest area is 0.9699. Move from 0.9699 to the left until you reach 1.8, and then move up from 0.9699 until you get to 0.08 (see Figure 40). Putting these values together, we get . In other words, the -value with area 0.03 to its right is .
    image
    Figure 6.42: FIGURE 40 Using the table to find a value of for a given area.

NOW YOU CAN DO

Exercises 79–86.