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A Test To Measure Self-control

A criminologist has developed a test to measure self-control. The test is normed so that it has a mean of 70 and a standard deviation of 20. The scores are normally distributed in the population of college students used to develop the test.
a. What is the percentile rank of a score of 40?
b What percentage of scores falls between 35 and 90?
c. What is the standard score for a test score of 65?
d. What proportion of students should score above 115?
e. What is the cutoff score below which 87% of all scores fall?

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