Question

5. Suppose that the average number of Facebook friends users have is normally distributed with a mean of 125 and a standard deviation of about 55. Assume fourteen individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

a. What is the distribution of x¯? x¯ ~ N( , ) ______

b. For the group of 14, find the probability that the average number of friends is less than 107. ___

c. Find the first quartile for the average number of Facebook friends. ____

6. The amount of syrup that people put on their pancakes is normally distributed with mean 57 mL and standard deviation 9 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( , ) ____

b. What is the distribution of x¯? x¯ ~ N( , ) ____

c. If a single randomly selected individual is observed, find the probability that this person consumes is between 57.7 mL and 59.2 mL. ____

d. For the group of 41 pancake eaters, find the probability that the average amount of syrup is between 57.7 mL and 59.2 mL ____

Answer 1