Math Problem Statement
The total area to the left of zequalsnegative 1.34 and to the right of zequals2.26 under the standard normal curve is
enter your response here. (Round to four decimal places as needed.)
Solution
To find the total area under the standard normal curve to the left of and to the right of , we can use the standard normal distribution table (Z-table) or a calculator.
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Area to the left of :
- From the Z-table, the area to the left of is approximately .
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Area to the right of :
- From the Z-table, the area to the left of is approximately .
- Therefore, the area to the right is .
-
Total area:
- The total area to the left of and to the right of is:
Thus, the total area is approximately 0.1023 (rounded to four decimal places).
Would you like any further details or explanations? Here are some related questions to consider:
- How do you interpret the areas under the normal curve?
- What is the significance of the standard normal distribution in statistics?
- Can you explain how to use a Z-table effectively?
- How do you calculate areas for other values of ?
- What is the relationship between -scores and probabilities?
Tip: When calculating areas under the curve, always remember to consider both tails and whether you're looking for areas to the left or right of specific -scores.
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Math Problem Analysis
Mathematical Concepts
Statistics
Probability
Standard Normal Distribution
Z-Scores
Formulas
Area under the standard normal curve
1 - P(Z < z) for right-tail probability
Theorems
Properties of the Standard Normal Distribution
Suitable Grade Level
Grades 10-12
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