A senior manager is interestedif age distributions of customers is different for two branches.One located in a major shopping centre and one located in a small shopping centre.100 random transactions are selected from each branch and age information is found for each associated customer. Table 1 shows the data in a crosstabs table. This table is also found in Assignment2: Q4 tab in the Excel file.

observed counts

Age Distribution

Less than 30 30 - 55 56 or older

Small shopping centre 20 40 40

Major shopping centre 30 50 20

Table 1: observed counts

Answer the following questions.Give all answers to a) - c) to 2 decimal places.

a)[1 mark] What is the probability that a customer did the transaction in a small shopping centre and is 56 years or over?

b)[1 mark]What is the probability that a customer did the transaction in a small shopping centre or is 30 - 55 years of age.

c)[1 mark]What is the probability that a customer did the transaction in a small shopping centre given they are less than 30 years?

d)[2 marks] Using Excel, provide a clustered bar chart that visualises the relationship between Location of branches and Age distribution.Without quoting any percentages, what does this chart suggest to you?

e)[10 marks] At a 5% significance level, is there a statistically significant association between Location of branches and Age distribution of customers?