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Question No. 1

Assume that the number of weekly study hours for students at a certain University is approximately normally distributed with a mean of 20 and a standard deviation of 8.

 

i. Find the probability that a randomly chosen student studies less than 10 hours per week.

 

ii. Estimate the percentage of students that study more than 35 per hours per week.

 

iii. A certain lecture group consists of 100 students. You may assume that this lecture group forms a simple random sample from the students in the university. Find the probability that the average number of study hours for this group is between 19 and 21 hours.

 

 

Question No. 2

A test is taken by some students, their marks are recorded and we are interested in the properties of the sample mean. Under the assumption that the marks follow a normal distribution with exact mean 65 and variance 144, calculate the probability that the mark of a randomly selected student.

 

i. Is greater than 67.5 exactly; and

ii. Lies between 63 and 67 exactly