A polygraph (lie detector) is an instrument used to determine if an individual is telling the truth. These tests are considered to be 82% reliable. In other words, if an individual lies, there is a 0.82 probability that the test will detect a lie. Let there also be a 0.010 probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions. a. What is the probability of a Type I error?b. What is the probability of a Type II error?

EXAMPLE: Turning 4/3 into an improper fraction
In order to turn an improper fraction into a mixed fraction, you need to find the closest number to multiply the denominator by to get the numerator (ex: 3 times 1 is the closest number to 4). Then you would subtract that number after it was multiplied (in this case 1x3= 3) from the original numerator (so 4-3 = 1.) The answer for this question is 1 and 1/3.
Another example: 15/4 is 3 and 3/4 as a mixed number because 15 divided by 4 is closest to 3 (3x4 is 12 and 3x5 is 15, which is too large) with a remainder of 3. The closest multiple is the whole number and the remainder is the new numerator.
Hope this helps! I'm sorry if it's confusing-- it's easier to explain with paper and pencil :)