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 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 26% of people have a pet bird, 56% of people have a pet dog and 9% of people have both a pet bird and a pet dog. (4 points) What is the probability that a person had a pet dog, given they had a pet bird? (4 points) What is the probability a randomly selected person had a pet bird or a pet dog? (3 points) What is the probability that a randomly selected person did not have a pet dog? (5 points) Are the events “having a pet bird” and “having a pet dog” independent? Show all work to support your claim. (5 points) Are the events “having a pet bird” and “having a pet dog” mutually exclusive? Show all work to support your claim.

Problem 6 (19 points): A certain pizzeria knows that to make…

Problem 6 (19 points): A certain pizzeria knows that to make a pizza, the distribution of the amount of sauce they use has a normal distribution with a mean of 6.8 ounces and a standard deviation of 1.8 ounces. (6 pts) If a pizza has too much sauce on it, the customers start to complain. The pizzeria notices that customers complain if they have the top 10% of sauce.  What is the amount of sauce used for this top 10% where the customers begin to complain? (6 pts) Suppose that in a single day, the bakery makes 36 pizzas. Describe the sampling distribution of the sample mean amount of sauce used throughout the day. (7 pts) What is the probability that the mean amount of sauce used for the 36 pizzas was between 7 and 8 ounces?