A sample of 12 Australian universities students scores on the universal cognitive ability and emotional intelligence test was conducted. The average score for this sample was 87 out of 100, placing Australian universities at 5th place in the world.

Although, there are 49 Australian universities and Ms CatrionaJacksonthe Chief Executive and Director of Universities Australia is concerned that the sample mean is unreliable. Given the population standard deviation is 10.75, conduct a 99% confidence interval of the mean score.