Question
Find the indicated probability using the standard normal distribution. \( P(z>-2.62) \) \( \frac{\text { Click here to view page } 1 \text { of the standard normal table. }}{\text { Click here to view page } 2 \text { of the standard normal table. }} \) \( P(z>-2.62)=\square \) (Round to four decimal places as needed.)
Ask by Chavez Medina. in the United States
Feb 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
P(z > -2.62) ≈ 0.9956
Solution
To find P(z > -2.62), we can use the symmetry of the standard normal distribution. Notice that:
P(z > -2.62) = P(z < 2.62)
Consult the standard normal table for z = 2.62. Typically, you will find:
P(z < 2.62) ≈ 0.9956
Thus,
P(z > -2.62) ≈ 0.9956
Rounded to four decimal places, the final answer is 0.9956.
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Simplify this solution The Deep Dive
To find \( P(z > -2.62) \), you can use the standard normal distribution table (also known as the z-table). First, look up the value for \( z = -2.62 \). The table will give you \( P(z < -2.62) \), which represents the area to the left of \(-2.62\). Since the total area under the standard normal curve is 1, you can find \( P(z > -2.62) \) using the formula: \[ P(z > -2.62) = 1 - P(z < -2.62) \] From the z-table, \( P(z < -2.62) \) is approximately 0.0043. Therefore: \[ P(z > -2.62) = 1 - 0.0043 = 0.9957 \] So: \[ P(z > -2.62) = 0.9957 \] (rounded to four decimal places).
