Find the indicated probability or percentage for the normality distributed variables?
A bank loan officer rates applicants for credit. The ratings are in general distributed with be determined of 200 and a Standard deviation of 50. If an applicants is randomly select, find the probability of a rating that is between 200 and 275?
Answers: For any common random adjustable X with niggardly μ and standard deviation σ , X ~ Normal( μ , σ ), (note that in most textbook and literature the notation is with the variance, i.e., X ~ Normal( μ , σ^2 ). Most software denotes the average with simply the standard deviation.)
You can translate into standard normal unit by:
Z = ( X - μ ) / σ
Moving from the standard normal subsidise to the original distribuiton using:
X = μ + Z * σ
Where Z ~ Normal( μ = 0, σ = 1). You can after use the standard normal cdf table to get probabilities.
If you are looking at the be a sign of of a sample, consequently remember that for any sample beside a large ample sample size the plan will be normally distributed. This is call the Central Limit Theorem.
If a sample of size is is drawn from a population beside mean μ and standard deviation σ next the sample average xBar is typically distributed
with suggest μ and standard deviation σ /√(n)
An applet for finding the values
http://www-stat.stanford.edu/~naras/jsm/...
calculator
http://stattrek.com/Tables/normal.aspx
how to read the tables
http://rlbroderson.tripod.com/statistics...
In this press we have
X ~ Normal( μx = 200 , σx^2 = 2500 )
X ~ Normal( μx = 200 , σx = 50 )
Find P( 200 < X < 275 )
= P( ( 200 - 200 ) / 50 < ( X - μ ) / σ < ( 275 - 200 ) / 50 )
= P( 0 < Z < 1.5 )
= P( Z < 1.5 ) - P( Z < 0 )
= 0.9331928 - 0.5
= 0.4331928
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Answers: For any common random adjustable X with niggardly μ and standard deviation σ , X ~ Normal( μ , σ ), (note that in most textbook and literature the notation is with the variance, i.e., X ~ Normal( μ , σ^2 ). Most software denotes the average with simply the standard deviation.)
You can translate into standard normal unit by:
Z = ( X - μ ) / σ
Moving from the standard normal subsidise to the original distribuiton using:
X = μ + Z * σ
Where Z ~ Normal( μ = 0, σ = 1). You can after use the standard normal cdf table to get probabilities.
If you are looking at the be a sign of of a sample, consequently remember that for any sample beside a large ample sample size the plan will be normally distributed. This is call the Central Limit Theorem.
If a sample of size is is drawn from a population beside mean μ and standard deviation σ next the sample average xBar is typically distributed
with suggest μ and standard deviation σ /√(n)
An applet for finding the values
http://www-stat.stanford.edu/~naras/jsm/...
calculator
http://stattrek.com/Tables/normal.aspx
how to read the tables
http://rlbroderson.tripod.com/statistics...
In this press we have
X ~ Normal( μx = 200 , σx^2 = 2500 )
X ~ Normal( μx = 200 , σx = 50 )
Find P( 200 < X < 275 )
= P( ( 200 - 200 ) / 50 < ( X - μ ) / σ < ( 275 - 200 ) / 50 )
= P( 0 < Z < 1.5 )
= P( Z < 1.5 ) - P( Z < 0 )
= 0.9331928 - 0.5
= 0.4331928