SUPPLEMENTARY EXERCISES for ... - WH Freeman

Section 1 41filter?S5.10 A bottling company uses a filling machine to fill plastic bottles with a popular cola. Thebottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to anormal distribution with mean µ = 298 ml and standard deviation σ = 3 ml.(a) What is the probability that an individual bottle contains less than 295 ml?(b) What is the probability that the mean contents of the bottles in a six-pack is less than 295ml?S5.11 Judy’s doctor is concerned that she may suffer from hypokalemia (low potassium inthe blood). There is variation both in the actual potassium level and in the blood test thatmeasures the level. Judy’s measured potassium level varies according to the normal distributionwith µ = 3.8 and σ = 0.2. A patient is classified as hypokalemic if the potassium level is below3.5.(a) If a single potassium measurement is made, what is the probability that Judy is diagnosedas hypokalemic?(b) If measurements are made instead on 4 separate days and the mean result is compared withthe criterion 3.5, what is the probability that Judy is diagnosed as hypokalemic?S5.12 The level of nitrogen oxides (NOX) in the exhaust of a particular car model varies withmean 0.9 grams per mile (g/mi) and standard deviation 0.15 g/mi. A company has 125 cars ofthis model in its fleet.(a) What is the approximate distribution of the mean NOX emission level x for these cars?(b) What is the level L such that the probability that x is greater than L is only 0.01?S5.13 The study habits portion of the Survey of Study Habits and Attitudes (SSHA) psychologicaltest consists of two sets of questions. One set measures “delay avoidance” and the othermeasures “work methods.” A subject’s study habits score is the sum X + Y of the delay avoidancescore X and the work methods score Y . The distribution of X in a broad population offirst-year college students is close to N(25, 10), while the distribution of Y in the same populationis close to N(25, 9).(a) If a subject’s X and Y scores were independent, what would be the distribution of the studyhabits score X + Y ?(b) Using the distribution you found in (a), what percent of the population have a study habitsscore of 60 or higher?(c) In fact, the X and Y scores are strongly correlated. In this case, does the mean of X + Ystill have the value you found in (a)? Does the standard deviation still have the value you foundin (a)?Chapter 6Section 1