Standard normal distribution is defined in normal distribution that is the special case of it. This distribution occurs when normal random variable has mean equal to zero and value of standard deviation is equal to one.
In the standard normal distribution the normal random variable is known as the standard score or also called as z – score. There is an expression through which every normal random variable ‘x’ can be transformed in z – score that is defined as follows:
z = (x - μ) / s,
The above formula defines the Standard Deviation Problems of normally distributed random variable.
Where ‘x’ is a variable, ‘μ’ define the mean and ‘s’defines the standard deviation of random variable ‘x’.
According to the above formula random variable is defined by subtracting the mean of the given distribution from the random variable that will be standardize for the distribution and then it will be divided by the standard deviation of the distribution. When we talk about the standardize random variable it has value of mean equal to zero and value of standard deviation equals to one. We can define it through the example if value of random variable equals to 40 means x = 40 and value of mean and standard deviation are 20 and 10 respectively then find the standardize value of x?
Solution: Given x = 40,
Mean (μ) = 20 and,
Standard deviation (s) = 10, then according to the formula
z = (x - μ) / s,
z= (40 –20) / 10,
z = 20 / 10,
z = 2,
So for the given example the standardize value that is also define as z – score of random variable 40 is 2.
In upcoming posts we will discuss about Line of best fit - least squares regression and Trigonometric form of complex numbers. Visit our website for information on Indian Certificate of Secondary Education
In the standard normal distribution the normal random variable is known as the standard score or also called as z – score. There is an expression through which every normal random variable ‘x’ can be transformed in z – score that is defined as follows:
z = (x - μ) / s,
The above formula defines the Standard Deviation Problems of normally distributed random variable.
Where ‘x’ is a variable, ‘μ’ define the mean and ‘s’defines the standard deviation of random variable ‘x’.
According to the above formula random variable is defined by subtracting the mean of the given distribution from the random variable that will be standardize for the distribution and then it will be divided by the standard deviation of the distribution. When we talk about the standardize random variable it has value of mean equal to zero and value of standard deviation equals to one. We can define it through the example if value of random variable equals to 40 means x = 40 and value of mean and standard deviation are 20 and 10 respectively then find the standardize value of x?
Solution: Given x = 40,
Mean (μ) = 20 and,
Standard deviation (s) = 10, then according to the formula
z = (x - μ) / s,
z= (40 –20) / 10,
z = 20 / 10,
z = 2,
So for the given example the standardize value that is also define as z – score of random variable 40 is 2.
In upcoming posts we will discuss about Line of best fit - least squares regression and Trigonometric form of complex numbers. Visit our website for information on Indian Certificate of Secondary Education
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