The ages of students at York University are normally distributed with a mean of 25 years and a standard deviation of 3.5 years. The ages of students at U of T follow a normal distribution with a mean of 27 years and a standard deviation of 2.5 years. It is believed that 40% of all students at York University say that they prefer to take online courses. a) Suppose a random sample of 100 students was taken at York University, what is the probability that the mean age is greater than 24? b) A random sample of 100 students was taken at York University. What is the probability that in the sample, less than 35% say that they prefer to take the online courses? c) A random sample of 30 York students and 30 U of T students were taken. What is the probability that the mean age of 30 randomly selected students from York University is less than the mean age of 30 randomly selected students from U of T? d) This part is independent of parts a) to c). A researcher collected data on the annual salary of professors in Ontario. He wishes to construct a confidence interval for the population mean annual salary. Which of the following statement(s) is true? You can pick more than one if necessary. I. A 98% confidence interval will have a greater chance of including the true mean salary than a 95% confidence interval. II. A 98% confidence interval will be narrower than a 95% confidence interval. III. A 98% confidence interval requires the researcher to take a larger sample