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Unformatted text preview: USING THE Z-TABLE Ex. 1) Find the area under the normal distribution curve. Between z=0 and z=0.75 Start by drawing the standard normal curve and shading the desired area. The shaded area looks like that in the chart. So, our answer will be the value we look up in the chart. The area (probability) is 0.2734 Ex 2) Find the area under the standard normal curve between z=0.79 and z=1.28. Start by drawing the standard normal curve and shading the desired area. The table gives 0 to 0.79 and 0 to 1.28. Subtracting the values from the tables gives us the shaded piece. *Same side b subtract 0.3997-0.2852 = 0.1145 Area/probability 0.1145 Ex. 3) Find the probability. P( z > 2.83) Start by drawing the standard normal curve and shading the desired area. From 0 all the way out is 0.5. The table gives from 0 to 2.83. Subtracting the two gives us the shaded area. 0.5-0.4977 = 0.0023 The probability (area) is 0.0023. Ex 4) Find the z value that corresponds to the given area. From 0 to the far right is 0.5 and the table gives from z to 0. Subtracting 0.8962 & 0.5 gives us the value inside the table for z to 0. 0.8962 0.5 = 0.3962. This is the area/probability. We still need the z-value. Looking inside the table and matching it to the z-value outside, the closest value is 1.26. This z-value is on the left. Remember the standard normal distribution is symmetric, so all we have to do is add a negative. z-value = -1.26 0.75 0 0.79 1.28 2.83 0.8962 0 1.63 2.36 0.36 2.06 2.06 2.06 DETERMINING NORMAL PROBABILITIES EX 1) The average daily jail population in the United States is 618,319. If the distribution is normal and the standard deviation is 50,200, find the probability that on a randomly selected day, the jail population is a) Greater than 700,000...
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This document was uploaded on 02/23/2010.
- Spring '09
- Normal Distribution