reference sheet three week 5 - 8 .pdf - Standard Normal...

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Standardizing the Sample Mean - With any normally distributed random variable X, we can standardize it to a standard normal distribution through the linear transformation: Standard Normal Table - The cumulative distribution function. For a particular value of Z it gives the area to the left under the probability density function. EXAMPLES - The online nutrition information at a famous fast food chain states that one of their burgers contains 980 mg of sodium. The amount of sodium in these burgers is approximately normally distributed with a mean of 980 mg and a standard deviation of 50 mg. 1. If a single burger of this type is randomly selected, what is the probability it contains more than 1000 mg of sodium? 2. If four burgers are randomly selected, what is the probability their average sodium content exceeds 1000 mg? Central Limit Theorem - Helps us in situations when the population is not normally distributed. Tells us that regardless the distribution of t he population, if the sample size (n) is large enough then the sampling distribution of x ̅ will be approximately normally distributed. More formally, as n increases, the sampling distribution of x ̅ approaches normality. HOW LARGE IS ENOUGH? n must be greater than 30 (rough guideline). EXAMPLE - Suppose that selling prices of houses in a large city are known to have a mean of $382,000 and a standard deviation of $150,000.

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