1) In a ballroom dance competition, each couple is identified by a number worn on the leader's back. At a recent competition, forty couples competed. Their numbers are listed below: 107 109 116 120 121 126 130 134 143 151 158 163 169 174 180 182 186 188 191 197 200 203 208 | 211 215 220 228 231 234| 241 | 246 253 256 262| 268 271 279 285 250 274 Dances at the competition are organized into heats, with each heat consisting of a particular group of dancers doing a particular dance. A portion of the Heat Schedule is given below, with the couples listed for twelve heats of Waltz, Foxtrot, and Quickstep: Heat 46 Waltz Heat 47 Foxtrot Heat 48 Quickstep 107 Heat 49 Waltz Heat 50 Heat 51 Foxtrot Quickstep 120 107 107 126 121 121 120 121 134 126 126 134 163 188 151 158 163 182 134 143 174 174 220 186 180 228 174 197 151 191 215 241 203 203 158 182 253 211 220 231 262 256 231 211 250 262 274 241 231 246 262 262 262 268 274 279 268 253 279 Heat 57 Heat 52 Waltz Heat 53 Foxtrot Heat 54 Heat 55 Waltz Heat 56 Quickstep Foxtrot Quickstep 109 109 109 109 109 109 143 180 188 126 134 120 191 121 116 116 134 163 126 180 174 186 158 211 191 180 220 200 200 228 200 215 231 211 211 231 231 231 253 241 231 215 250 250 253 250 228 274 256 262 268 256 231 279 262 274 285 262 246 285

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Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.