The Chamber of Commerce in a Canadian city has conducted an evaluation of restaurants in its metropolitan area. Each restaurant received a rating on a -point scale on typical meal price (least expensive to most expensive) and quality (lowest quality to greatest quality). A crosstabulation of the rating data is shown. Forty-two of the restaurants received a rating of on quality and on meal price, of the restaurants received a rating of on quality and on meal price, and so on. Forty - eight of the restaurants received the highest rating of on both quality and meal price. Meal Price (y) Quality (x ) 1 2 3 Total 1 42 39 3 84 2 30 63 54 147 3 3 18 48 69 Total 75 120 105 300 a. Develop a bivariate probability distribution for Quality and Meal Price of a randomly selected restaurant in this Canadian city. Let quality rating and meal price. Round your answers to two decimal places. Meal Price Quality Total 0.14 0.13 0.01 0.28 0.10 0.21 0.18 0.49 0.01 0.06 0.16 0. Total 0.25 0.40 0.35 1 b. Compute the expected value and variance for quality rating,. 1.98 (Round your answer to two decimal places) 0.52 (Round your answer to four decimal places) c. Compute the expected value and variance for meal price, . 2.09 (Round your answer to two decimal places) 0.59 (Round your answer to four decimal places) d. Your assistant has computed the variance of:. Compute the covariance of and. Round your answer to four decimal places. 0.2818 What can you say about the relationship between quality and meal price? As quality increases, price increases Is this what you would expect? Yes e. Compute the correlation coefficient between quality and meal price? Round your answer to four decimal places. 0.5088 What is the strength of the relationship? Moderately positive Do suppose it is likely to find a low cost restaurant in this city that is also high quality? Yes