The amount of coffee that people drink per day is normally distributed with a mean of 14 ounces and a standard deviation of I" ounces. 31 randomly selected people are surveyed. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ MI 14 fl-:1 cl"F b. What is the distribution of it? it ~ Nfl 14 v', 1.5313 )1 ] of c. What is the probability that one randomly selected person drinks between 13.? and 14.1 ounces of coffee per day?| [1.11228 V" of d. For the 32 peoplmility that the average coffee consumption is between 13.11r and 14.1 ounces of coffee per day. I 131.1231} I o' e. For part d}, is the assumption that the distribution is normal necessary? 1. Find the IQR for the average of 32 coffee drinkers. o1 =| 13.1554 Jiounces o\" {13 = | 14.8346 \"'i ounces of Ion: [1.5692 | ounces of 2 The amount of syrup that people put on their pancakes is normally distributed with 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 ~ N( 55 169 X b. What is the distribution of D? I ~ N( 55 4.1220 X c. If a single randomly selected individual is observed, find the probability that this person consumes is between 52.5 ml and 53.5 mL. |0.0303 d. For the group of 41 pancake eaters, find the probability that the average amount of syrup is between 52.5 mL and 53.5 mL. 0.1209 e. For part d), is the assumption that the distribution is normal necessary? Yes NoThe lengths of adult males' hands are normally distributed with mean 185 mm and standard deviation is 7.5 mm Suppose that 44 individuals are randomly chosen. Round all answers to 4 where possible. a. What is the distribution of i\"? 1: e N( 136 b. For the group of 44, find the probability that the average hand length is less than 137' I 0 9615 x/l o' c. Find the third quartile for the average adult male hand length for this sample size. l 185 7626 \\ll 0' d. For part b), is the assumption that the distribution is normal necessary? cr' 4 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 T? X ~ N( 169 1 16.9 x b. For the group of 40, find the probability that the average price is between $167 and $169. 0.1867 c. Find the first quartile for the average textbook price for this sample size. $ 166.2 x (round to the nearest cent) d. For part b), is the assumption that the distribution is normal necessary? . Yes No ofQuestion 5 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 observed 43 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( 46 484 X b. What is the distribution of T? I ~ N( 46 11.2558 X C. What is the distribution of x? Y x - N( 1978 20812 X d. If one randomly selected student is timed, find the probability that this student's time will be between 48 and 50 minutes. |0.0359 e. For the 43 students, find the probability that their average time studying is between 48 and 50 minutes. 0.1590 f. Find the probability that the randomly selected 43 students will have a total study time more than 1849 minutes. 0.8144 g. For part e) and f), is the assumption of normal necessary? . Yes No h. The top 10% of the total study time for groups of 43 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? 2162.88 minutes ofThe 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 E? X ~ N( 21.5 5.766 x b. What is the distribution of ) x? > x - N( 322.5 1297.35 X C. P(T > 341.973) = 0.2944 h. For part c) and e), is the assumption of normal necessary? No Yes ofTreat the number of months X after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - U b. Suppose that 38 people are surveyed. What is the distribution of T for this sample? I ~ N( c. What is the probability that the average birth month of the 38 people will be less than 5.9