[10 marks]Island Mix Restaurant and Lounge is located in heart of Pickering, Ontario. Away from the Caribbean Islands, the relaxing environment takes the clients back to the distant islands of fun, cheer and delectable dishes. The financial analyst wants to determine the proportion of vegetarian orders. To do so, the financial analyst randomly selected 95 orders and found out that 28 of these were about vegetarian dishes.

(a) What is the value of the population proportion? (1 mark)

(b) What is the best estimate of the population proportion? How is that value called? (2 marks)

(c) What assumptions can you make about the shape of the distribution. Why? (2 marks)

(d) Develop an 86% confidence interval for the population proportion (3 marks)

(e) Interpret the meaning of the results in part (d). (2 mark)