WORD PROBLEMS: 1. The lengths of a particular species of worm are normally distributed with a mean of 21 em and standard deviation of 1.5 cm. Find the probability that a worm selected at random 15: a. Less than 23.4 cm long b. More than 19.8 cm long c. Between 18 cm and 24 cm long 2. The length oftirne patients have to wait in Dr. Booth's waiting room us known to be normally distributed with mean 14 minutes and standard deviation 4 minutes. Find the probability that a patient will have to wait more than 20 minutes to see the doctor. What proportion of the patients wait less than 10 minutes? 3. Packets of breakfast cereal are said to contain 550g. The manufacturer knows that the weights are normally distributed with mean 551.2g and standard deviation 15 g. What proportion of packets will contain more than the stated weight? 4. A biologist has studied a particular tropical insect and she has discovered that its lifespan is normally distributed. The mean lifespan of this insect is 'i'2 days and the standard deviation of its lifespan is eight days. Find the probability that the next insect studied lives: a. Fewer than 7'0 days b. Between 68 and 1'8 days c. More than 26 days 5. The heights of the girls in a particular college is normally distributed with mean 166 cm and standard deviation 4 cm. Find the probability that if a student is chosen at random her weight will be: a. Less than 165 cm b. Between 163 and 168 cm c. More than ITO cm 6. The lengths of metal bolts are normally distributed with mean ,u cm and standard deviation 7 cm. If 2.5% of the bolts measure more than 68 cm. nd the value of a. 7. The average weekly incomes, in 5, of 18 selected occupations in the United Kingdom were: bi\" q 244, 146, 228, 396, 435, 641, 577, 122, 294 yr 35?, 802 730, 286, 484, 169,, 559, 208, 498 / U ?f 3. Find the median, mode, variance, range, mad, upper extreme, lower extre b. Draw a box plot to represent these incomes. --___.~______, [ W\" e. Calculate the mean weekly income and the standard deviation. b ml