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To compute probability value using normal distribution

Robinson & Associates does employment screening for large companies in southern California.  It typically follows two-step process.  First potential applicants are assumed a test that covers basic knowledge and intelligence.  If applicants score among a certain ranges, they are called in for an interview.  If they score under a certain point they are sent a rejection letter.  If applicants score overhead a certain point, they are sent straight to the client's human resources office without the interview.  Recently Robinson & Associates instigated working with a new client and formulated a new test just for this company.  Thirty people were specified the test which is theoretical to produce scores that are distributed according to a bell-shaped distribution.  The following data reproduce the scores of those 30 people.
































Robinson and Associates has in the past issued a rejection letter with no interview to the lower 16% taking the test.  They as well send the upper 2.5% directly to the company without an interview.  Everybody else is interviewed.  Based on the data as well as the assumption of a bell-shaped distribution, what score must be used for the two cut-offs?

Statistics and Probability, Statistics

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