deviation of x to 5? Explain to someone who knows nothing about statistics the measurement to reduce the standard advantage of of a single measurement. reporting the average of several measurements rather than the result A sample of young men, continued. Suppose that the blood cholesterol levels of all men age 20 to 34 years follows the Normal distribution with mean per deciliter (mg/dl) and standard deviationo =41 mg/dl. M = u = 188 milligrams 13.5 NG DISTRIBUTIONS (a) Choose an SRS of 100 men from this population. What is the sampling dis- tribution of x? What is the probability that ī takes a value between 185 and 191 mg/dl? This is the probability that x estimates u within +3 mg/dl. (b) Choose an SRS of 1000 men from this population. Now what is the probability that x falls within +3 mg/dl of u? The larger sample is much more likely to give an accurate estimate of THE CENTRAL LIMIT THEOREM The facts about the mean and standard deviation of x are true no matter what Quno 13 5(a) shows the density

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The Z-score tells you the number of standard deviations away from the mean (and in what X-μ can be used to find the Z-score for a direction) a data value is. The formula: Z single member of the population. Notice X - μ tells you the signed distance the data value (X) is from the mean. When you divide that by the size of each chunk (the standard deviation) you are measuring the distance in units of the size of the standard deviations (how many standard deviations fit in the distance between the data value and the mean) - which gives you the Z-score. The formula X = μ+Z-o can be used to find the value in the population when given the Z-score (signed number of standard deviations). Notice that Z. tells you how far from the mean the data value is (since Z is the number of standard deviations and o is the size of each standard deviation the product tells the total distance). So adding the distance from the mean to the mean gives the location along the number line for the data value. A…

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