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# A researcher has conducted a study among the students in a local university. The information is recorded in the data set on page 5. Use the data set to answer ALL questions. All workings must be shown

A researcher has conducted a study among the students in a local university. The information is recorded in the data set on page 5. Use the data set to answer ALL questions. All workings must be shown.Question 1 (40 marks)a.                Construct the probability distribution of the number of students who are wearing spectacles when three students are randomly selected from this university. Hence, calculate the mean. Interpret the value of the mean. [8 marks]b.               Construct the 98% confidence interval of the time spent exercising by all students who wear spectacles.                                                                                                                          [8 marks]c.                Calculate the probability that less than 5 of the 11 students selected who like black colour. [8  marks]d.               Find the probability that a randomly selected student will dine out at least 2 or more times a day.[8  marks]e.                Calculate the probability that the age of a selected female student is aged between 20 and 24 years old. State your assumption(s) made.[8  marks]