Determine the area under the standard normal curve between z = -1.53 and 0.
Thank you
To determine the area under the standard normal curve between z = -1.53 and z = 0, we need to use a standard normal distribution table or calculator.
Step 1: Look up the area to the left of z = -1.53 in the standard normal distribution table.
The area to the left of z = -1.53 is 0.0630.
Step 2: Look up the area to the left of z = 0 in the standard normal distribution table.
The area to the left of z = 0 is 0.5000.
Step 3: Calculate the area between z = -1.53 and z = 0.
The area between z = -1.53 and z = 0 is the difference between the two areas calculated in Step 1 and Step 2:
Area = 0.5000 - 0.0630 = 0.4370
Therefore, the area under the standard normal curve between z = -1.53 and 0 is approximately 0.4370.
To determine the area under the standard normal curve between two z-values, we will use the standard normal distribution table.
Step 1: Find the area to the left of z = -1.53
The standard normal distribution table provides the cumulative probability to the left of a given z-value. Look for the closest z-value in the table, which in this case is -1.5. The value in the table for -1.5 is 0.0668. Since -1.53 is slightly smaller than -1.5, we can assume that the area to the left of -1.53 is also approximately 0.0668.
Step 2: Find the area to the left of z = 0
Again, refer to the standard normal distribution table. The z-value 0 is at the center of the distribution, so the cumulative probability to the left is 0.50.
Step 3: Calculate the area between the two z-values
To determine the area between the two z-values, subtract the area to the left of -1.53 from the area to the left of 0.
Area = 0.50 - 0.0668 = 0.4332
Therefore, the area under the standard normal curve between z = -1.53 and 0 is approximately 0.4332.