99.7% will fall within three Standard Deviation Normal Distribution two types of random variables – Discrete Random Variables - (count things) for example, number for heads in a 10 coin flip, number of females of democrats in a sample. Continuous Random Variable : on measurements) unaccountability infinite number of values (values – within an interval on the real line) many possible values. For example, time to complete a task, exam score complete a task is continuous because it can – take you 5 min 3 hours not a specific time to count (continuous). – A continuous random variable X has a normal distribution if its value falls into a smooth (continuous) curve with a bell-shaped pattern. Changing an x-value to a z-value z-formula – STEPS: To find Probabilities for a Normal Distribution Draw a picture of the distribution Translate the problem into one of the following: p(X<a), p(X>b), or p(a<X<b). Shade the area on your picture. Standardize to a Z score formula using the Z-formula: Z=x- µ/σ Look up the z-score on the Z-Table and find its corresponding probabilities (USE Z-TABLE) 5a. If you need a than” probability (p(X<a) you are done) “less 5b.If you need a than” probability p(X>b) take 1- result from step 4. “greater If you need a probabilities that is, p(a<X<b) do Steps “between –two-values” – – 1-4 for b (the larger of the two values) and again for a (the smallest of the two and subtract the results) Standard Normal Probability Distribution A random variable that has a normal distribution with properties of mean (μ) = 0 and a standard deviation (σ) =1, has a standard normal probability Letter designates this particular normal random variable. distribution. z Example Mean (μ) =18 Standard deviation (σ) =6 If P(x 22) =? ≥
99.7% will fall within three Standard Deviation Normal Distribution – two types of random variables Discrete Random Variables - (count things) for example, number for heads in a 10 coin flip, number of females of democrats in a sample. Continuous Random Variable : – on measurements) unaccountability infinite number of values (values within an interval on the real line) many possible values. For example, time to complete a task, exam score – complete a task is continuous because it can take you 5 min – 3 hours not a specific time to count (continuous). A continuous random variable X has a normal distribution if its value falls into a smooth (continuous) curve with a bell-shaped pattern. Changing an x-value to a z-value – z-formula STEPS: To find Probabilities for a Normal Distribution Draw a picture of the distribution Translate the problem into one of the following: p(X<a), p(X>b), or p(a<X<b). Shade the area on your picture. Standardize to a Z score formula using the Z-formula: Z=x- µ/σ Look up the z-score on the Z-Table and find its corresponding probabilities (USE Z-TABLE) 5a. If you need a “less than” probability (p(X<a) you are done) 5b.If you need a “greater than” probability p(X>b) take 1- result from step 4. If you need a “between –two-values” probabilities – that is, p(a<X<b) – do Steps 1-4 for b (the larger of the two values) and again for a (the smallest of the two and subtract the results) Standard Normal Probability Distribution A random variable that has a normal distribution with properties of mean (μ) = 0 and a standard deviation (σ) =1, has a standard normal probability distribution. Letter z designates this particular normal random variable. Example Mean (μ) =18 Standard deviation (σ) =6 If P(x ≥ 22) =?
SOM307_STUDYGUIDE.docx