Question

Answer the following using the appropriate z-score table. a.) What is the area to the left of the z-score z=−0.86? (round answer to four decimal places) The area is approximately_____ b.) What is the area to the left of the z-score z=1.54 ? (round answer to four decimal places) The area is approximately_____ c.) Determine the area to the right of the z-score z=1,54 (to four decimal places). The area is approximately____ d.) Determine the area between the z-scores z=−0.86 and z=1.54 (to four decimal places). The area is approximately___

Answer 1

`\bold{ANSWERS:}`

a) To find the area to the left of the z-score z = -0.86, we need to look up the corresponding value in the z- score table. The table provides the area under the standard normal curve to the left of a given z-score.

Looking up -0.86 in the z-score table, we find that the area to the left of z = -0.86 is approximately 0.1949.


b) Similarly, to find the area to the left of the z-score z = 1.54, we consult the z-score table.

The table shows that the area to the left of z = 1.54 is approximately 0.9382.


c) To determine the area to the right of the z-score z = 1.54, we subtract the area to the left of z = 1.54 from 1 (since the total area under the curve is equal to 1).

Using the value from the previous part, the area to the right of z = 1.54 is approximately 1 - 0.9382 = 0.0618.


d) To find the area between the z-scores z = -0.86 and z = 1.54, we subtract the area to the left of z = -0.86 from the area to the left of z = 1.54.

Using the values from the previous parts, the area between z = -0.86 and z = 1.54 is approximately 0.9382 -0.1949= 0.7433.