The proportion of observations from a standard normal distribution that take values less than 1.15 is about?
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For any normal random variable X with mean μ and standard deviation σ , X
~ Normal( μ , σ ),
standard normal units can be translated by
Z = ( X - μ ) / σ
Where Z ~ Normal( μ = 0, σ = 1). standard normal CDF tables to get probabilities can be used.
If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem.
If a sample of size is drawn from a population with mean μ and standard deviation σ then the sample average xBar is normally distributed
with mean μ and standard deviation σ /√(n)
~ Normal( μ , σ ),
standard normal units can be translated by
Z = ( X - μ ) / σ
Where Z ~ Normal( μ = 0, σ = 1). standard normal CDF tables to get probabilities can be used.
If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem.
If a sample of size is drawn from a population with mean μ and standard deviation σ then the sample average xBar is normally distributed
with mean μ and standard deviation σ /√(n)
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