Math Problem Statement
Z is the standard normal variable. Find the indicated probability. (Round your answer to four decimal places.)
P(0 ≤ Z ≤ 0.6)
Solution
To find the probability for a standard normal variable , follow these steps:
Step 1: Look up cumulative probabilities in the Z-table.
The Z-table provides the cumulative probability from the leftmost tail to a given Z-value.
- P(Z ≤ 0): Since the Z-table is symmetric, .
- P(Z ≤ 0.6): From the Z-table, the value for is 0.7257.
Step 2: Calculate .
Since is the area between and , we subtract:
Final Answer:
Would you like further explanation on using Z-tables, or do you have additional questions?
Here are 5 related questions:
- What is the probability for ?
- How do you compute ?
- What is the total area under the standard normal curve?
- How can we use the Z-table to find ?
- How does symmetry help when computing probabilities for Z-values around 0?
Tip: Always subtract cumulative probabilities carefully to avoid calculation errors when finding areas between two Z-values.
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Math Problem Analysis
Mathematical Concepts
Probability
Statistics
Standard Normal Distribution
Z-Score
Formulas
P(a ≤ Z ≤ b) = P(Z ≤ b) - P(Z ≤ a)
Standard Normal Distribution formula
Theorems
Properties of the Standard Normal Distribution
Symmetry of the Normal Curve
Suitable Grade Level
Grades 10-12
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