Find the area under the standard normal curve between -1.32 and the mean, P(-1.32 < z < 0.00). (Give your answer correct to four decimal places.)
To find the area under the standard normal curve between -1.32 and 0.00, we can use the standard normal distribution table or a statistical calculator.
1. Standardize the values:
First, we need to standardize the given values (-1.32 and 0.00) using the formula:
z = (x - μ) / σ
Since we are dealing with the standard normal distribution, the mean (μ) is 0 and the standard deviation (σ) is 1.
For -1.32:
z1 = (-1.32 - 0) / 1 = -1.32
For 0.00:
z2 = (0 - 0) / 1 = 0
2. Look up the values in the standard normal distribution table:
Next, we need to find the area corresponding to these standardized values in the standard normal distribution table. The table provides the areas under the curve for different z-scores.
The area between -1.32 and 0.00 can be found by subtracting the area corresponding to -1.32 (z1) from the area corresponding to 0.00 (z2).
From the standard normal distribution table, we can find the area to the left of z1 (-1.32) is 0.0934 and the area to the left of z2 (0.00) is 0.5000.
Therefore, the area between -1.32 and 0.00 is:
Area = 0.5000 - 0.0934 = 0.4066
So, the area under the standard normal curve between -1.32 and the mean (P(-1.32 < z < 0.00)) is approximately 0.4066 (rounded to four decimal places).