g MATH'I127: Introduction to Statistics (Asynchronous (100% Online)) 20337 Chapter 7: The Central Limit Th . Questien 'i The average time te run the 5K fun run is 24 minutes are randomly selected to run the 5K fun run. Round a assume a normal distribution. a. What is the distribution of X? X ~ N( , b. What is the distribution of 5:? E ~ N( , J) and the standard deviation is 2.7 minutes. ll answers c. What is the distribution of Z 3:? Z .7: ~ NC], ) d. If one randomly selected runner is timed, find the 23.4154 and 23.8154 minutes. [ l e. For the 48 runners, find the probability that their average time is between 23.4154 and 23.3154 minutes. [ f. Find the probability that the randomly selected 48 person team will have a total time me than 1128. ' J g, Fer part e) and f), is the assumption of normal necessary? 0 N00 Yea IL The top 10% of all ~13 person team relay races will compete in the champiqnship' mums. These white 10% lowest times, What is the {gs-3st total time that a relay team scam have and still nukeit Ruhr ' probability that this runner's time will be between WP round? minutes MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 ... Chapter 7: The Central Limit Theorem Chapter 7: 0 Chapter 7: Central Limit Theorem (Sums) Score: 0/5 0/5 answered Question 2 Each sweat shop worker at a computer factory can put together 4.6 computers per hour on average with a standard deviation of 0.8 computers. 13 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X ~ N( b. What is the distribution of a? X - N( c. What is the distribution of _ ? ) = - N d. If one randomly selected worker is observed, find the probability that this worker will put together between 4.3 and 4.6 computers per hour. e. For the 13 workers, find the probability that their average number of computers put together per hour is between 4.3 and 4.6. f. Find the probability that a 13 person shift will put together between 61.1 and 63.7 computers per hour . g. For part e) and f), is the assumption of normal necessary? @ Yes No h. A sticker that says "Great Dedication" will be given to the groups of 13 workers who have the top 20% productivity. What is the least total number of computers produced by a group that receives a sticker ? computers per hour (round to the nearest computer) IMG_20221202_20....jpg IMG_20221202_20....jpg IMG_20221202_20....jpg IMG_20221201_19....jpg Type here to search OMATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 ... Chapter 7: The Central Limit Theorem Chapter 7: Central Limit Theorem (Sums) Score: 0/5 0/5 answered Question 3 Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 41 minutes and standard deviation 17 minutes. A researcher observed 13 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of a? a ~ N( c. What is the distribution of ? ~ ~d d. If one randomly selected student is timed, find the probability that this student's time will be between 35 and 42 minutes. e. For the 13 students, find the probability that their average time studying is between 35 and 42 minutes. f. Find the probability that the randomly selected 13 students will have a total study time more than 520 minutes. g. For part e) and f), is the assumption of normal necessary? @ Yes No h. The top 15% of the total study time for groups of 13 students 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? minutes IMG_20221202_20....jpg - IMG_20221202_20...jpg IMG_20221202_20....jpg - IMG_20221201_19. Type here to search OMATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 ... Chapter 7: The Central Limit Theorem Score: 0/5 0/5 answered Question 4 The average amount of money that people spend at Don Mcalds fast food place is $7.9700 with a standard deviation of $1.9400. 48 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X ~ N( b. What is the distribution of ac? a ~ N( c. What is the distribution of ) ? _ x - N d. What is the probability that one randomly selected customer will spend more than $8.0900? e. For the 48 customers, find the probability that their average spent is less than $8.0900. f. Find the probability that the randomly selected 48 customers will spend less than $388.3200. g. For part e) and f), is the assumption of normal necessary? ( No Yes h. The owner of Don Mcalds gives a coupon for a free sundae to the 5% of all groups of 48 people who spend the most money. At least how much must a group of 48 spend in total to get the free sundae? $ Hint. IMG_20221202 20....jpg IMG_20221202_20....jpg IMG_20221202_20....jpg IMG_20221201_19.MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 ... Chapter 7: The Central Limit Theorem Chapter 7: Central Limit Theorem (Sums) Score: 0/5 0/5 answered Question 5 The average score for games played in the NFL is 22.2 and the standard deviation is 9.1 points. 44 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of a? I ~ N( b. What is the distribution of ) .? _at Nd c. P(3 > > 987.4568) = h. For part c) and e), is the assumption of normal necessary? O Yes No Hint: Some Helpful Videos: IMG_20221202_20....jpg - IMG_20221202_20....jpg IMG_20221202 20....jpg IMG_20221201_19....jpg Type here to search