Math Problem Statement
Find the indicated area under the standard normal curve. To the left of equals negative 0.88 and to the right of z equals0.88
Solution
To solve this, we need to calculate two areas under the standard normal curve:
- The area to the left of
- The area to the right of
The total area under the standard normal curve equals 1 (or 100%).
1. Area to the left of
From standard normal distribution tables or using a calculator, the cumulative probability to the left of is approximately 0.1894.
2. Area to the right of
The cumulative probability to the left of is 0.8106. So, the area to the right of is:
Total Area
Since the areas to the left of and to the right of are equal, we can calculate the total area by summing these two areas:
Thus, the total area under the standard normal curve to the left of and to the right of is approximately 0.3788.
Would you like more details or have any questions about the steps?
Here are five related questions you might find helpful:
- What is the area between two z-scores, like between and ?
- How do you calculate the area under the normal curve for any given z-value?
- How does the symmetry of the normal distribution simplify these types of problems?
- Can you find the area for z-values beyond 3 standard deviations?
- How do z-scores relate to probabilities in a normal distribution?
Tip: Using a z-table or calculator is a quick way to find cumulative areas under the normal curve.
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Math Problem Analysis
Mathematical Concepts
Statistics
Standard Normal Distribution
Z-scores
Probability
Formulas
Cumulative area under the normal curve
P(Z < z) = cumulative probability for a given z-value
P(Z > z) = 1 - cumulative probability for a given z-value
Theorems
Symmetry of the normal distribution
Empirical rule for normal distributions
Suitable Grade Level
Grades 11-12, College Level
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