The heights of a certain group is known to follow a normal distribution with expected value and variance 2 . A researcher surveyed 50 individuals from the population. The sample mean of the height is 179.8 cm and the sample standard deviation is 7.10 cm. The researcher wants to know that if the average height of the group is 185 cm or not. (a) Define in words the random variable X when X N(, 2 ). (1 p) (b) Construct a 95% confidence interval for the parameter and interpret your results: could the average height be 185 cm? (2 p) (c) Test, at the 0.01 level of significance that could the average height be 185 cm? List all steps of the test. (3 p)