STATISTICAL TECHNIQUES AND TOOLS
Z DISTRBUTION
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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31.7%
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34%
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50%
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68%
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Detailed explanation-1: -For the standard normal distribution, the value of the mean is equal to zero (=0), and the value of the standard deviation is equal to 1 (=1). The random variable that possesses the standard normal distribution is denoted by z.
Detailed explanation-2: -Empirical Rule or 68-95-99.7% Rule In any normal distribution with mean and standard deviation : Approximately 68% of the data fall within one standard deviation of the mean. Approximately 95% of the data fall within two standard deviations of the mean.
Detailed explanation-3: -Answer. In order to find the unknown mean and standard deviation , we code by the change of variables ↦ = − . Now ∼ 0, 1 follows the standard normal distribution and ( ≤ 7 2 . 4 4 ) = ≤ 7 2 .