Find the area under the standard normal curve which lies between z = +1.25
and z = +2.11
To find the area under the standard normal curve between z = +1.25 and z = +2.11, we can use the standard normal distribution table or a statistical software.
Using the standard normal distribution table, we can find the area corresponding to each z-value and then subtract the smaller area from the larger area.
1. Find the area left of z = +1.25:
- The standard normal distribution table provides the area left of a given z-value.
- From the table, the area left of z = +1.25 is approximately 0.8944.
2. Find the area left of z = +2.11:
- From the table, the area left of z = +2.11 is approximately 0.9834.
3. Calculate the area between z = +1.25 and z = +2.11:
- Subtract the smaller area from the larger area calculated in steps 1 and 2:
Area between z = +1.25 and z = +2.11 = 0.9834 - 0.8944 = 0.0890
Therefore, the area under the standard normal curve between z = +1.25 and z = +2.11 is approximately 0.0890.
To find the area under the standard normal curve between two specific z-values, we can use a standard normal distribution table or a computer software/statistical calculator.
However, I'll explain how to calculate it using a standard normal distribution table.
Step 1: Draw a standard normal curve and shade the area between the two z-values (+1.25 and +2.11).
Step 2: Look up the z-value +1.25 in the standard normal distribution table. The table will give you the cumulative probability to the left of this z-value, which is 0.8944.
Step 3: Look up the z-value +2.11 in the standard normal distribution table. The table will give you the cumulative probability to the left of this z-value, which is 0.9821.
Step 4: Subtract the cumulative probability for +1.25 from the cumulative probability for +2.11: 0.9821 - 0.8944 = 0.0877.
The result of 0.0877 represents the area under the standard normal curve between z = +1.25 and z = +2.11, or in other words, the probability that a randomly selected value falls between these two z-values.
David Lane normal distribution