Find the area under the standard normal curve that lies between z = -2.09 and z = 1.98. Note: the graph may not be drawn to scale.
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To find the area under the standard normal curve between two specific z-scores, we need to use a standard normal distribution table or a calculator.
Step 1: Look up the area to the left of z = -2.09 in the standard normal distribution table. The area to the left of -2.09 is 0.0188.
Step 2: Look up the area to the left of z = 1.98 in the standard normal distribution table. The area to the left of 1.98 is 0.9767.
Step 3: Subtract the smaller area from the larger area to find the area between the two z-scores:
0.9767 - 0.0188 = 0.9579
Therefore, the area under the standard normal curve between z = -2.09 and z = 1.98 is 0.9579.
To find the area under the standard normal curve between two z-scores, we need to use the standard normal distribution table or a calculator that can perform this calculation.
The standard normal distribution table provides the area to the left of a given z-score. Since we want to find the area between two z-scores, we will need to find two values from the table and calculate the difference between them.
1. Start by finding the area to the left of z = -2.09.
- Look up the z-score -2.09 in the standard normal distribution table.
- The table will provide the area to the left of -2.09, which is 0.0174 (rounded to four decimal places).
2. Next, find the area to the left of z = 1.98.
- Look up the z-score 1.98 in the standard normal distribution table.
- The table will provide the area to the left of 1.98, which is 0.9767 (rounded to four decimal places).
3. Finally, calculate the area between the two z-scores.
- Subtract the area to the left of z = -2.09 from the area to the left of z = 1.98.
- 0.9767 - 0.0174 = 0.9593 (rounded to four decimal places).
Therefore, the area under the standard normal curve that lies between z = -2.09 and z = 1.98 is approximately 0.9593.