4-20 H-20 -30 -3 -2 -1 0 1 2 3 In particular, we need to find the a and b values that take # to 0, u + o to 1, u + 20 to 2, etc. One way of finding this is by solving the following equations for a and b: y= ax+b = y=1x-IM 0 = au + 6 7 b = - am 3 = X -M 1 = a( # + 0) +6 = 1 = gu+ 08+ (-au) 1 = a6 3 a= 1 x b = - ( 8 ) m- JM =b/ If your transformed date was The particular linear transformation of a normal distribution described above has a special name, it gives us a z-score. It tells us how many called Z instead we are away from the A z-score for a data value r can be determined by: r - mean I- H or stand. dev.' or Z =axtb 2= Z= Xu 3. Data set X has mean I = 20 and standard deviation s = 4. Find the z-score and interpret its meaning. (a) x = 20 (b) x = 10 for any data (c) = = 40 value x = Z=X-M 4. Outliers and z-scores. Recall the probability density function that describes the normal curve 1