"Denkopdrachten" Normaalverdeling We write N(m,s) to denote a normal dist. with mean m and standard deviation s. So the IQ test is N(100,16) and Dutch men's height is N(181,6) (in cm). Then make sure you can do the following. 1. Given N(100,16) convert the following to Z-scores: 92, 132, 164, 90 2. Given N(181cm,6cm) convert the following heights to Z-scores: 187 cm, 172 cm, 181 cm, 160 cm 3. Given N(100,16), what percentile do the following scores fall on? 108, 96, 120, 88 4. Given that Dutch women aged 18-24 jr. have a normal height distribution with mean 172cm and sd 6cm, what percentage of them will have heights in the following range? a. between 166 cm and 178 cm (abbreviated: 166 <= h <= 178) b. up to 175 cm (<= 175) c. more than 180 cm (> 180) d. 160 <= h <= 180 5. Only the "top p%" have a chance of winning a scholarship. a. What is the top 10% of a N(100,16) distribution? b. What is the top 5% of a N(500,100) distribution? 6. The bottom 5% of a satisfaction survey should be checked carefully. The survey had a near normal distribution of N(3.1,0.7) Which satisfaction scores will lead to further checking? 7. Mass-market clothing manufacturers ignore the 5% of the population with extreme sizes (the 2.5% very small and 2.5% very large). What consequences does this have in the following cases? a. Men's shoe size is N(43,2.5) What men have to buy shoes in specialty shops? b. Women's hat size is N(6.75, 0.25). Which women are forced to buy expensive hats?