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A group of students at University of Bedfordshire took a test in Marketing and they needed to score 50 to pass. The results showed that the final grades have a mean of 62 and a standard deviation of 8. Suppose we can approximate the distribution of these grades by a normal distribution. Based on this information, you are required to perform the following: 

(a) What percentage (to 3 decimal places) of the students scored more than 78? 

(b) What percentage (to 3 decimal places) of the students scored under 50? 

(c) What percentage (to 3 decimal places) of the students scored between 60 and 89? 

(d) Draw a normal distribution curve for each of the above ((a)-(c)), showing clearly the X, Z and the shaded region.


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