May I please have a detailed explanation for how to answer these? I have a Ti-84 plus calculator. Thank you!

I Suppose that the average number of Facebook friends users have is normally distributed with a mean of 135 and a standard deviation of about 53. Assume six individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible. a. What is the distribution of 5:? 5T: N( .,, l) b. For the group of 6, find the probability that the average number of friends is more than 150. c. Find the first quartile for the average number of Facebook friends. ' d. For part b), is the assumption that the distribution is normal necessary? 0 N00 Yes 2) The amount of coffee that people drink per day is normally distributed with a mean of 14 ounces and a standard deviation of 5.5 ounces. 32 randomly selected people are surveyed. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ Ni'r Il J b. What is the distribution of a? a - Nil c. What is the probability that one randomly selected person drinks between 13.8 and 14.3 ounces of coffee per day? l I d. For the 32 people, find the probability that the average coffee consumption is between 13.8 and 14.3 ounces of coffee per day. l e. For part d), is the assumption that the distribution is normal necessary? 0 N00 Yes f. Find the IQR for the average of 32 coffee drinkers. Q1 =' 'ounces Q3 = l ' ounces IQR: ' ' ounces deviation 1.3 month. 15 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible. 3) Suppose the age that children learn to walk is normally distributed with mean 13 months and standard a. What is the distribution of X? X ~ N(I , I) I) c. What is the probability that one randomly selected person learned to walk when the person was between 11.5 and 14 months old? I I b. What is the distribution of it? :2:- N(I I, d. For the 15 people, find the probability that the average age that they learned to walk is between 11. 5 and 14 months old I I e. For part d), is the assumption that the distribution is normal necessary? O YesO No . Find the IQR for the average first time walking age for groups of 15 people. Q1 = months Q3 = r I months -'h IQR: I I months 4) The average production cost for major movies is 69 million dollars and the standard deviation is 20 million dollars. Assume the production cost distribution is normal. Suppose that 17 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(I II I) ,. I) c. For a single randomly selected movie, find the probability that this movie's production cost is b. What 15 the distribution of :E? w N(I J between 68 and 70 million dollars I I d. For the group of 17 movies, find the probability that the average production cost is between 68 and 70 million dollars. I e. For part (1), is the assumption of normal necessary? 0 YesO No 5) The average score for games played in the NFL is 22 and the standard deviation is 9.2 points. 47 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of 5:? i ~ Nd L- ') b. What is the distribution of Z :33? Z 33 ~ N(' c. P(:E 1122.689)=: l h. For part c) and e), is the assumption of'jnormal necessary? 0 YesO No 6 Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 43 minutes and standard deviation 16 minutes. A researcher observed 45 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ M" l) b. What is the distribution of 5:? 5: ml .,:') c. What is the distribution of Z 3:? Z :3 N ',[ L) d. If one randomly selected student is timed, find the probability that this student's time will be between 40 and 42 minutes. ' l e. For the 45 students, find the probability that their average time studying' is between 40 and 42 minutes. ' f. Find the probability that the randomly selected 45 students will have a total study time more than 1890 minutes. I l g. For part e) and f), is the assumption of normal necessary? 0 YesO No h. The top 10% of the total study time for groups of 45 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 7 A computer selects a number X from 1 to 7 randomly and uniformly. Round all answers to 4 decimal places where possible. a. What' is the distribution of X? X~ U(i } b. Suppose that the computer randomly picks 38 such numbers. What is the distribution of :E for this i) c. What is the probability that the average of 38 numbers will be less than 4.1? } selection of numbersa: N(. J