Question 1 (1 point) P(X=x)= [x/6 for x =1, 2, or 3 0 otherwise. The probability model for the random variable X is specified above. Notice that each value of x is associated with a probability. What is the expected value of this discrete random variable? O 1 2.33Question 2 (1 point) In a linear regression model, calculate the slope of the line, b1, when the correlation coefficient is r= O.46, and the standard deviations of the predictor variable equals Sm 20.200 and the standard deviation of the response variable equals 8y 20.200. Note: 1 Only round your final answer to 2 decimal places. Enter your final answer with 2 decimal places. Your Answer: Answer Question 3 (1 point) Assuming y is the dependent variable and x is the independent variable in a linear relationship, what is the slope of the line of best fit if 'r' = 0.70, By = 6.57, and 5x = 2.86. Note: 1- Only round your final answer to 2 decimal places. Enter your final answer with 2 decimal places. Your Answer: Answer Question 4 (1 point) Consider the following linear model: A y = 9.5 + 1.7x This linear model forecasts total number of books sold (in 1.0005 books) given the total amount of preorder sales (in $1,000) identified by variable x. Calculate the total predicted number of books sold if the amount of pre-order sales is $1000. Hint: Remember :13 is measured in $1000s and 3:! is measured in 1,000s books sold. However, the question is asking for the predicted number of books sold (how many books). Your Answer: Answer Question 5 (1 point) Assume that we have a regression model szO-l-blx The average values are 3 =2 and 5 =2. The standard deviations are 8y 20.41 and 81; 22.01. Also, the correlation is 7\" 2040. What is the predicted value for A the response variable (y) if the value for the explanatory variable (a?) is zero? Note: 1 Round any intermediate numbers to 4 decimal places. 2 Round your final answer to 2 decimal places. Enter your final answer with 2 decimal places. Your Answer: Question 6 (1 point) What is the y if the yintercept and slope of the line of best fit are 29 and 2.0, respectively, and the average of the values in the explanatory variable is 852.1? (assume y represents the response variable) Note: 1- Only round your final answer to 2 decimal places. Enter your final answer with 2 decimal places. Your Answer: Answer Question 7 (1 point) In linear regression, assume that a unit change in Zm leads to a change of 0.34 in g. What is the value of the correlation coefficient representing the relationship between x and y? Note: 1 Enter your answer with 2 decimal places. Your Answer: Answer Question 8 (1 point) In a batch of recently manufactured parts there are 17 identical parts of which 6 are defective. We select one part from the batch at random and realize that it is defective. Now without replacing the first part in the batch again, we pick a second part from the batch. What is the probability that the second part is defective? Note: 1- Express the probability as a decimal number. Round your final answer to 2 decimal places. For example, % = 0. 142857 will be entered as 0.14. Your Answer: l; Answer Question 9 (1 point) A certain Nike store records the behaviour of all customers for a week to see how likely it is that they will buy a pair of shoes from the new display. Among the 1653 people observed, they figure out that the probability of a customer making a purchase is 52.5%. What is the probability that a customer doesn't make a purchase? Notes: 1- Enter your answer with 1 decimal places. 2 Report the probability as a percentage. However, do n_ot use the percentage symbol in your answer. For instance, if the answer is 65.3%, only enter 65.3. Your Answer: Answer Question 10 (1 point) On average, each insurance claim forwarded to a certain division of an insurance company has a 53% chance of getting approved after the preliminary review. In addition to that, all claims forwarded to this office are assumed to be independent of each other. Suppose on a given day 5 claims are forwarded to this office. What is the probability that at least one of the 5 claims will be approved after the preliminary review? Notes: 1 Your final answer should be expressed as a decimal and not a percentage. 2 Only round your final answer to 4 decimal places. Enter your final answer with _l decimal places. Your Answer: Answer Question 11 (1 point) Sally works at a bookstore. Out of boredom, she keeps track of the number of men and women who visit the store, and the type of book they purchase. The results of her research based on today's numbers are summarized in the table below: | Fiction Non-Fiction Men 55 42 | Women 44 42 Based on her numbers, what is the probability that a customer selected at random purchased a nonfiction book, given (knowing) that the customer is a woman? Note: 1 Only round your final answer to 2 decimal places. Enter your final answer with 2 decimal places. Your final answer should be in the decimal form and not the fraction 1 form. For example, 7 = 0. 142857 will be entered as 0.14. Your