Question
Find the closest z-value such that 80% of the total area lies to the left of it.
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GPT 3.5
To find the closest z-value such that 80% of the total area lies to the left of it, we need to use the standard normal distribution table or a calculator.
In a standard normal distribution, the mean (μ) is 0 and the standard deviation (σ) is 1. The area to the left of a given z-value represents the cumulative probability.
Since we want 80% of the total area to lie to the left of the z-value, the cumulative probability (P(X ≤ Z)) is 0.8.
Using a standard normal distribution table or a calculator, we can find the z-value associated with a cumulative probability of 0.8. The closest z-value is approximately 0.8416.
Therefore, the closest z-value such that 80% of the total area lies to the left of it is 0.8416.
In a standard normal distribution, the mean (μ) is 0 and the standard deviation (σ) is 1. The area to the left of a given z-value represents the cumulative probability.
Since we want 80% of the total area to lie to the left of the z-value, the cumulative probability (P(X ≤ Z)) is 0.8.
Using a standard normal distribution table or a calculator, we can find the z-value associated with a cumulative probability of 0.8. The closest z-value is approximately 0.8416.
Therefore, the closest z-value such that 80% of the total area lies to the left of it is 0.8416.
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