Chapter 7: Central Limit Theorem (Mean) The amount of coffee that people drink per day is normally distributed with a mean of 14 ounces and a standard deviation of 7 ounces. 32 randomly selected people are surveyed. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( b. What is the distribution of ? ~ ~ N( c. What is the probability that one randomly selected person drinks between 13.7 and 14.1 ounces of coffee per day? d. For the 32 people, find the probability that the average coffee consumption is between 13.7 and 14.1 ounces of coffee per day. e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes f. Find the IQR for the average of 32 coffee drinkers. Q1 = ounces Q3 = ounces IQR: ouncesChapter 7: Central Limit Theorem (Mean) lb" The amount of syrup that people put on their pancakes is normally distributed 1with mean 55 mL and standard deviation 13 mL. Suppose that 41 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ Ml: H I} . . l1 c. If a single randomly selected individual is observed, find the probability that this person consumes is between 52.5 mLand 55.5 mL.| | J b. What is the distribution or o? o ~ N{| d. For the group of 41 pancake eaters, find the probability that the average amount of syrup is between 51.5mLend 53.5mL.| | e. For part d}, is the assumption that the distribution is normal necessary? C? Yes'' No Chapter E": Central Limit Theorem (Mean) Question 3 The lengths of adult males' hands are normally distributed with mean 135 mm and standard deviation is 15 mm. Suppose that 44 individuals are randomly chosen. Round all answers to 4 where possible. I :1 a. 1|.I'-.I'hat is the distribution of it? it ~ N{ b. For the group of 44, find the probability that the average hand length is less than 18?. I I c. Find the third quartile for the average adult male hand Length for this sample size. I I d. For part b}, is the assumption that the distribution is normal necessary? '33:} No' Yes Chapter 7: Central Limit Theorem (Mean) 14 The average price of a college math textbook is $169 and the standard deviation is $26. Suppose that 40 textbooks are randomly chosen. Round all answers to 4 decimal places where possible. a. What is the distribution of D? C - N( b. For the group of 40, find the probability that the average price is between $167 and $169. c. Find the first quartile for the average textbook price for this sample size. 5 (round to the nearest cent) d. For part b), is the assumption that the distribution is normal necessary? O YesO NoChapter I": Central Limit Theorem (Mean) 1:"? answered Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 46 minutes and standard deviation 22 minutes. A researcher obsewed 43 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? I ~ NII l1 )' b. What is the distribution of it? it ~ N{I c. What is the distribution of 23:? Zn: n I II :I} d. If one randomly selected student is timed find the probability that this student's time will be between 43 and 5E1 minutes. I I e. For the 43 students, find the probability that their average time studying is between 48 and 50 minutes. I I f. Find the probability that the randomly selected 43 students will have a total study time more than 1849 minutes. I I g. For part e] and f], is the assumption of normal necessary?'-._ ."I"es-:.-' No h. The top 1055 of the total study time for groups of 43 studenE will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker? Iminutes Chapter 7: Central Limit Theorem (Mean) )/7 6 The average score for games played in the NFL is 21.5 and the standard deviation is 9.3 points. 15 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of C? C - N( b. What is the distribution of C. P(C 341.973) = h. For part c) and e), is the assumption of normal necessary? O NoO YesChapter 7: Central Limit Theorem (Mean) 0/7 answered 7 Suppose that the age of students at George Washington Elementary school is uniformly distributed between 6 and 11 years old. 37 randomly selected children from the school are asked their age. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - U( Suppose that 37 children from the school are surveyed. Then the sampling distribution is b. What is the distribution of C? C - N( c. What is the probability that the average of 37 children will be between 8 and 8.3 years old