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Distributions & Random Variables
Watch comprehensive video reviews for Distributions & Random Variables, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
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SL 4.12
Standardization converts any normal distribution into the standard normal distribution, which has a mean μ of 0 and a standard deviation σ of 1. To standardize, we calculate the z-score, defined as
which measures how many standard deviations a value x lies above or below the mean. This allows us to directly compare values from different normal distributions using a common reference scale.
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Basically, we shift the normal distribution so that it is centered at zero, then stretch or squeeze it so it has a standard deviation of 1.
Example: finding μ
The random variable follows a normal distribution X∼N(μ,7). Given that P(X<60)=0.8, find μ.
On the standard normal distribution N(0,1), the area is 0.8 when z=invNorm(0.8, 0, 1) =0.84162. So
Example: finding σ
The random variable X follows a normal probability distribution X∼N(11,σ). Given that P(22<X)=0.4, find σ.
If P(22<X)=0.4 then P(X<22)=1−0.4=0.6.
On the standard normal distribution N(0,1), the area is 0.6 when z=invNorm(0.6, 0, 1) =0.253347. So
SL 4.12
Standardization converts any normal distribution into the standard normal distribution, which has a mean μ of 0 and a standard deviation σ of 1. To standardize, we calculate the z-score, defined as
which measures how many standard deviations a value x lies above or below the mean. This allows us to directly compare values from different normal distributions using a common reference scale.
Powered by Desmos
Basically, we shift the normal distribution so that it is centered at zero, then stretch or squeeze it so it has a standard deviation of 1.
Example: finding μ
The random variable follows a normal distribution X∼N(μ,7). Given that P(X<60)=0.8, find μ.
On the standard normal distribution N(0,1), the area is 0.8 when z=invNorm(0.8, 0, 1) =0.84162. So
Example: finding σ
The random variable X follows a normal probability distribution X∼N(11,σ). Given that P(22<X)=0.4, find σ.
If P(22<X)=0.4 then P(X<22)=1−0.4=0.6.
On the standard normal distribution N(0,1), the area is 0.6 when z=invNorm(0.6, 0, 1) =0.253347. So