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The area (in percentage) under standard normal distribution curve of random variable Z within limits from −3 to +3 is _________.
Correct answer is '99.6'. Can you explain this answer?
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Most Upvoted Answer
The area (in percentage) under standard normal distribution curve of r...
A to b is given by:
$\displaystyle \frac{1}{\sqrt{2\pi}} \int_{a}^{b} e^{-\frac{x^2}{2}} dx$
This integral cannot be solved analytically, so it is usually approximated using numerical methods or tables. The tables provide the area under the curve for different values of Z, and we can use them to find the area between any two values of Z. For example, if we want to find the area between Z = -1.5 and Z = 2.2, we look up the values of the cumulative distribution function (CDF) for Z = -1.5 and Z = 2.2 in the standard normal distribution table and subtract them:
$P(-1.5 < z="" />< 2.2)="\Phi(2.2)" -="" />
where $\Phi(z)$ is the CDF of the standard normal distribution. We can also use software, such as Excel or R, to calculate the area under the curve for any given limits.
$\displaystyle \frac{1}{\sqrt{2\pi}} \int_{a}^{b} e^{-\frac{x^2}{2}} dx$
This integral cannot be solved analytically, so it is usually approximated using numerical methods or tables. The tables provide the area under the curve for different values of Z, and we can use them to find the area between any two values of Z. For example, if we want to find the area between Z = -1.5 and Z = 2.2, we look up the values of the cumulative distribution function (CDF) for Z = -1.5 and Z = 2.2 in the standard normal distribution table and subtract them:
$P(-1.5 < z="" />< 2.2)="\Phi(2.2)" -="" />
where $\Phi(z)$ is the CDF of the standard normal distribution. We can also use software, such as Excel or R, to calculate the area under the curve for any given limits.
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The area (in percentage) under standard normal distribution curve of r...
A standard normal distribution has zero mean and unit variance. A standard normal curve has 99.7% area in limits −3 to +3:
A standard normal curve (as shown in figure) has 68% area in limits −1 to +1,95% area is limits −2 to +2 and 99.7% area is limits −3 to +3 is 99.6.
Hence, the correct answer is 99.6.
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The area (in percentage) under standard normal distribution curve of random variable Z within limits from −3 to +3 is _________.Correct answer is '99.6'. Can you explain this answer?
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