What is the Approximated Value of \Phi(x) for x>3.5 in a Normal Distribution?

In summary, the value of \Phi(x) for a normal distribution when x > 3.5 is not a finite number and will always be less than 1. The values may get very close to 1, but the difference is insignificant for most situations. The statement that \Phi(x) = 0.5 is false, as the only value that satisfies this equation is x = 0.
  • #1
DamjanMk
4
0
Hi,
I'd like to know the value that [tex]\Phi(x)[/tex] of a normal distribution is approximated when x> 3,5.
I assume it is 1, since the value for x=3,49 is 0,9998...
But I got some answers at the university that it might be 0,5

Thanks
 
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  • #2
There is no finite value of for which it is 1: that is, if you calculate precisely, it will always be the case that [itex] \Phi(x) < 1 [/itex] for a finite number [itex] x [/itex]. For example, [itex] \Phi(4) \approx 0.9999683 [/itex] and [itex] \Phi(5) \approx 0.9999997 [/itex] (calculation from R software). However, just like my two examples, the values essentially get so close to 1 that the difference is, for almost all situations, immaterial.

For your second comment ("But I got some answers at the university that it might be 0,5") - if you mean 0.5, that is definitely false: the only value that gives [itex] \Phi(x) = 0.5 [/itex] is
[itex] x = 0 [/itex].
 
  • #3
Thank you :)
 

FAQ: What is the Approximated Value of \Phi(x) for x>3.5 in a Normal Distribution?

What is the formula for the normal distribution for x>3.5?

The formula for the normal distribution for x>3.5 is f(x) = (1/σ√(2π))e^-(x-μ)^2/2σ^2, where μ is the mean and σ is the standard deviation.

How is the normal distribution for x>3.5 different from the standard normal distribution?

The normal distribution for x>3.5 is a specific type of normal distribution where the values of x are greater than 3.5. This means that the curve will be shifted to the right, with a higher probability of values falling within this range. The standard normal distribution, on the other hand, has a mean of 0 and a standard deviation of 1, and is used to standardize any normal distribution curve.

What does the area under the normal distribution curve represent?

The area under the normal distribution curve represents the probability of a random variable falling within a certain range of values. This is known as the probability density function, and the total area under the curve is always equal to 1.

How can the normal distribution for x>3.5 be used in real life?

The normal distribution for x>3.5 can be used to model and analyze data in many fields, such as economics, psychology, and physics. It is particularly useful in analyzing data that follows a bell-shaped curve, such as test scores, heights, and weights.

Can the normal distribution for x>3.5 be skewed?

Yes, the normal distribution for x>3.5 can be skewed if the mean and standard deviation are not properly chosen. Skewness occurs when the data is not evenly distributed around the mean, resulting in a longer tail on one side of the curve. This can affect the accuracy of the data analysis and should be taken into consideration when using the normal distribution for x>3.5.

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