For any normal random variable X with mean ÎĽ and standard deviation Ď , X ~ Normal( ÎĽ , Ď ), (note that in most textbooks and literature the notation is with the variance, i.e., X ~ Normal( ÎĽ , Ď² ). Most software denotes the normal with just the standard deviation.)
You can translate into standard normal units by:
Z = ( X - ÎĽ ) / Ď
Moving from the standard normal back to the original distribuiton using:
X = ÎĽ + Z * Ď
Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities.
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 is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed
with mean ÎĽ and standard deviation Ď /âš(n)
IYou can translate into standard normal units by:
Z = ( X - ÎĽ ) / Ď
Moving from the standard normal back to the original distribuiton using:
X = ÎĽ + Z * Ď
Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities.
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 is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed
with mean ÎĽ and standard deviation Ď /âš(n)
IYou can translate into standard normal units by:
Z = ( X - ÎĽ ) / Ď
Moving from the standard normal back to the original distribuiton using:
X = ÎĽ + Z * Ď
Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities.
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 is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed
with mean ÎĽ and standard deviation Ď /âš(n)
in You can translate into standard normal units by:
Z = ( X - ÎĽ ) / Ď
Moving from the standard normal back to the original distribuiton using:
X = ÎĽ + Z * Ď
Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities.
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 is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed
with mean ÎĽ and standard deviation Ď /âš(n) in this question we have
X ~ Normal( ÎĽx = 1000 , Ďx² = 2500 )
X ~ Normal( ÎĽx = 1000 , Ďx = 50 )
Find P( X > 1150 )
P( ( X - ÎĽ ) / Ď > ( 1150 - 1000 ) / 50 )
= P( Z > 3 )
= P( Z < -3 )
= 0.001349898
Find P( X < 1100 )
P( ( X - ÎĽ ) / Ď < ( 1100 - 1000 ) / 50 )
= P( Z < 2 )
= 0.9772499
