All prospective employees of the U.S. Treasury Department are required to pass a special civil service examination before they are hired. Over a period of time the examination scores have been normally distributed, with a mean of m=85 and a standard deviation of s=4. Suppose that a large number of applicants for jobs with the Treasury Department sit for the test. a. What proportion can be expected to obtain an examination score of 90 or greater? b. An examination score of less than 80 is considered as failing. What is the probability that an individual will fail the examination? c. If we randomly select 3 examinations from this large applicant pool, what is the probability that all three examination scores will exceed 93?
All prospective employees of the U.S. Treasury Department are required to pass a special civil service examination before they are hired. Over a period of time the examination scores have been
a. What proportion can be expected to obtain an examination score of 90 or greater?
b. An examination score of less than 80 is considered as failing. What is the probability that an individual will fail the examination?
c. If we randomly select 3 examinations from this large applicant pool, what is the probability that all three examination scores will exceed 93?
d. If we randomly select 15 examinations from this large pool of applicants, what is the probability that the average of the 15 scores will exceed 85?
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