Question

Z follows a standard normal distribution. What is the area corresponding to P(−0.5< Z <0.75)? Round your answers to 4 decimal places.

Answer 1

To calculate the area under the curve for P(-0.5 < Z < 0.75), find the areas to the left of Z = 0.75 and Z = -0.5 using a Z-table, and subtract the latter from the former.

Step-by-step explanation:

To find the area under the standard normal curve corresponding to P(-0.5 < Z < 0.75), we need to calculate the area to the left of Z = 0.75 and subtract the area to the left of Z = -0.5 from it.

First, use the Z-table to find the area to the left of Z = 0.75. Assuming this area is represented by A1.

Next, find the area to the left of Z = -0.5. Let's call this A2.

The area you are looking for is A1 - A2. If for example A1 = 0.7734 (hypothetical value) and A2 = 0.3085 (hypothetical value), then the area between these Z-scores, P(-0.5 < Z < 0.75), would be 0.7734 - 0.3085 = 0.4649.

Round the final answer to four decimal places as the question specifies.