Question

Find the area under the standard normal distribution curve between z=0 and z=−2.53. Use The Standard Normal Distribution Table and enter the answer to 4 decimal places. The area between the two z values is____________-

Answer 1

To find the area under the standard normal distribution curve between z=0 and z=−2.53, subtract the area to the left of z=−2.53 from the area to the left of z=0.

Step-by-step explanation:

To find the area under the standard normal distribution curve between z=0 and z=−2.53, we can use the Standard Normal Distribution Table. The table provides the area to the left of each z-score. The area to the left of z=0 is 0.5, and the area to the left of z=−2.53 is 0.4948. To find the area between these two z-scores, we subtract the smaller area from the larger area: 0.5 - 0.4948 = 0.0052. Therefore, the area between z=0 and z=−2.53 is 0.0052.

Answer 2

The area between the two Z values is 0.4943

Using the Zscore values given ;

• Z = 0
• Z = -2.53

Using the standard normal distribution table ;

Area under the curve , P(x < 0) = 0.500

Area under the curve , P(x < -2.53) = 0.5000 - 0.0057

The area between the two values can be calculated thus;

• P(Z < 0) - P(Z < -2.53)

Now we have ;

P(Z < 0) - P(Z < -2.53) = 0.5000 - 0.0057

= 0.4943