The number of cars that pass by the entrance of a shopping mall, on average, is seven cars per minute. a. What is the probability that six or eight cars pass by the entrance of the shopping mall in a given minute? (3 Marks) b. What is the likelihood that no less than three cars pass by the entrance of the shopping mall in a given minute (round off your answer to 5 decimal places)? (5 Marks) c. What is the standard deviation of the number of cars that pass by the entrance of the shopping mall in a given hour period? ( 4.1 A researcher wants to establish the actual proportion of visitors that pay tribute to the statue of the king before they enter the museum. The researcher interviews 428 randomly selected visitors and found that 384 visitors have paid tribute to the statue of the king. Assume the proportion of visitors that pay tribute to the statue of the king are normally distributed. Note @90%: critical value: 1.645 @95%: critical value: 1.96 @99%: critical value: 2.58 a. What is the 90% confidence interval estimation for the proportion of visitors that pay tribute to the statue of the king before they enter the museum? (4 Marks) b. What is the 99% confidence interval estimation for the proportion of visitors that pay tribute to the statue of the king before they enter the museum? (2 Marks) c. What is the significant difference between the 90% and 99% confidence intervals in your previous answers? A homeware store wants to know whether the proportion of their customers who have the buyer's card (Yes or No) is the same across three major areas (Alberton, Bedfordview and Centurion). A random sample of 160 customers across the three major areas was selected and the number who had the buyer's cards was recorded. a. Can the manager conclude that the proportion of customers with a buyer's card per area is the same across the three areas? Test this assertion statistically at the 5% significance level. (6 Marks) Note @10%: critical value: 4.605 @5%: critical value: 5.991 @1%: critical value: 9.201 The statistic package shows that the chi-test stat= 5.991. b. If one tests the hypothesis with the 10% and 1% levels of significance, what would be your conclusion for each significance level (provide a conclusion with motivation for each significance level)