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The Australian Bureau of Statistics (ABS) has collected data on the part-time employment patterns of full-time...

The Australian Bureau of Statistics (ABS) has collected data on the part-time employment patterns of full-time students in Australia and has found the hours worked to be well approximated by a normal distribution with a mean of 15 hours.

(a) If 10% of students work more than 25 hours per week, what is the standard deviation of the number of hours worked by students?

(b) What is the probability that a student chosen at random works between 5 and 25 hours per week?

(c) What is the number of hours worked per week in order to be in the top 20 percentile?

(d) Suppose that student asks all the members of his/her tutorial group how many hours they work and that there are 36 students in the group. What is the probability that the average number of hours worked is between 5 and 25? State clearly any assumptions you make.

(e) Explain whether it is necessary to assume that the distribution of hours worked is normal when calculating part (d)? If the population standard deviation as determined in (a) is not known, what would be the best estimate.

Math   Statistics-And-Probability   
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