\f(a) The graph shows a Standard Normal Distribution. You are given 1 or 2 z-score(s) and need to shade the area (=probability) corresponding to: P( 0.5 Suppose that the average number of Facebook friends users have is normally distributed with a mean of 143 and a standard deviation of about 60. Assume twelve individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible. a. What is the distribution of i? 52 ~ N( , ) b. For the group of 12, find the probability that the average number of friends is less than 157. c. Find the third quartile for the average number of Facebook friends. d. For part b), is the assumption that the distribution is normal necessary? O N00 Yes 0 Question 2 v I The amount of syrup that people put on their pancakes is normally distributed with mean 61 mL and standard deviation 11 mL. Suppose that 13 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( , ) b. What is the distribution of :E? 5?: ~ N( , ) c. If a single randomly selected individual is observed, find the probability that this person consumes is between 65.2 mL and 67.9 mL. d. For the group of 13 pancake eaters, find the probability that the average amount of syrup is between 65.2 mL and 67.9 mL. e. For part d), is the assumption that the distribution is normal necessary? 0 YesO No 0 Question 5 v 293.473) = h. For part c) and e), is the assumption of normal necessary? 0 YesO No 0 Question 6 v Suppose that the age of students at George Washington Elementary school is uniformly distributed between 5 and 10 years old. 36 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 36 children from the school are surveyed. Then the sampling distribution is b. What is the distribution of is? 5: ~ N( , ) c. What is the probability that the average of 36 children will be between 7 and 7.2 years old