Z-score The z-score The Normal Distribution Definition of the Standard Normal Distribution The Standard Normaldistribution follows a normal distribution and has mean 0 and standard deviation 1 Notice that the distribution is perfectly symmetric about 0. If a distribution is normal but not standard, we can convert a value to the Standard normal distribution table by first by finding how many standard deviations away the number is from the mean. The The number of standard deviations from the mean is called the z-score and can be found by the formula x - m z = s Example Find the z-score corresponding to a raw score of 132 from a normal distribution with mean 100 and standard deviation 15.
Solution We compute 132 - 100 z = = 2.133 15 Example A z-score of 1. Automotive Craftsman Repair Tool. 7 was found from an observation coming from a normal distribution with mean 14 and standard deviation 3. Find the raw score. Solution We have x - 14 1.7 = 3 To solve this we just multiply both sides by the denominator 3, (1.7)(3) = x - 14 5.1 = x - 14 x = 19.1 The z-score and Area Often we want to find the probability that a z-score will be less than a given value, greater than a given value, or in between two values. To accomplish this, we use the from the textbook and a few properties about the normal distribution.
Psychology And Work Today 10th Edition Free Pdf. BlackSite Area 51 [Region Free/RUS] BlackSite. [RegionFree/RUSSOUND], Call Of Duty 4 Modern warfare [PAL/RUSSOUND], Kane & Lynch. The z-score and Area. Often we want to find the probability that a z-score will be less than a given value, greater than a given value, or in between two values.
Example Find P(z. Z.00.01.02.03.04.05.06.07.08.09 2.2.9861.9864.9868.9871.9875.9878.9881.9884.9887.9890 2.3.9893.9896.9898.9901.9904.9906.9909.9911.9913.9916 2.4.9918.9920.9922.9925.9927.9929.9931.9932.9934.9936 The columns corresponds to the ones and tenths digits of the z-score and the rows correspond to the hundredths digits. For our problem we want the row 2.3 (from 2.3 7) and the row.07 (from 2.3 7). The number in the table that matches this is.9911. Hence P(z 1.82) Solution In this case, we want the area to the right of 1.82.
This is not what is given in the table. We can use the identity P(z >1.82) = 1 - P(z 1.82) = 1 -.9656 =.0344 Example Find P(-1.18.
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