Problem 3 (19 points): A recent poll found that 57% of peopl…

Problem 3 (19 points): A recent poll found that 57% of people dress up in costumes for Halloween.  Suppose we take a random sample of 28 people and record how many of them dress up for Halloween. (6 pts) What probability distribution is this? Show all necessary work to support your claim. (6 pts) What is the probability exactly 18 of the people dress up for Halloween? (7 pts) What is the probability between 10 and 16, inclusive, of the people dress up for Halloween?

Problem 4 (21 points):   Based on a survey, it was found tha…

Problem 4 (21 points):   Based on a survey, it was found that 72% of people have a pet cat, 26% of people have a pet bird and 7% of people have both a pet cat and a pet bird. (4 points) What is the probability that a person had a pet bird, given they had a pet cat?  (4 points) What is the probability a randomly selected person had a pet cat or a pet bird? (3 points) What is the probability that a randomly selected person did not have a pet bird? (5 points) Are the events “having a pet cat” and “having a pet bird” independent? Show all work to support your claim. (5 points) Are the events “having a pet cat” and “having a pet bird” mutually exclusive? Show all work to support your claim.

Problem 3 (19 points): A recent poll found that 28% of peopl…

Problem 3 (19 points): A recent poll found that 28% of people enjoy going to haunted houses.  Suppose we take a random sample of 30 people and record how many of them enjoy haunted houses. (6 pts) What probability distribution is this? Show all necessary work to support your claim. (6 pts) What is the probability exactly 9 of the people enjoy haunted houses? (7 pts) What is the probability between 4 and 10, inclusive, of the people enjoy haunted houses?

Problem 5 (15 points): A tutoring center allows students to…

Problem 5 (15 points): A tutoring center allows students to make appointments for up to 60 minutes.  Let the random variable X represent the amount of time that the student spends stays for tutoring, and assume that all time intervals of equal length are equally likely. (4 points) What is the probability distribution for the random variable X? (5 points) Graph the distribution. (6 points) What is the probability that a student stays for tutoring between 31 and 48 minutes?