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junior college 2 | H2 Maths
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Which formula in Gaussian normal model do I use to get the answer shown in this question?
Can show how the formula is used?
Date Posted: 4 years ago
Views: 472
What is to be solved for in the first place? Standard deviation?
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Not really sure what's being asked here, but from the image it shows the solution for when P(x<0.91) = 0.818
This can be derived from the Normal Distribution Function as given, which takes conditions of standard deviation and mean, in order to generate a Normal distribution of the appropriate scale.
The conventional use of Z rather than X is with respect to the Standard Normal Distribution, N(0,1), where standard deviation is 1 and the mean is 0. By substituting these in, we get a monovariate equation for the Standard Normal Function, which is the curve plotted in the image I've provided.
By integrating for the probability density for continuous values below 0.91 i.e. (from negative infinity to 0.91), we obtain the integral equal to 0.5 (from negative infinity to zero) + the integral from 0 up to 0.91. By using definite integrals, we can find that this is 0.318, which sums to a probability density of 0.818.
Feel free to ask if there's more questions with regards to the above!
This can be derived from the Normal Distribution Function as given, which takes conditions of standard deviation and mean, in order to generate a Normal distribution of the appropriate scale.
The conventional use of Z rather than X is with respect to the Standard Normal Distribution, N(0,1), where standard deviation is 1 and the mean is 0. By substituting these in, we get a monovariate equation for the Standard Normal Function, which is the curve plotted in the image I've provided.
By integrating for the probability density for continuous values below 0.91 i.e. (from negative infinity to 0.91), we obtain the integral equal to 0.5 (from negative infinity to zero) + the integral from 0 up to 0.91. By using definite integrals, we can find that this is 0.318, which sums to a probability density of 0.818.
Feel free to ask if there's more questions with regards to the above!
Date Posted:
4 years ago
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