The probability that an automobile being filled with gasoline also needs an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and the filter need changing is 0.10. (a) If the oil has to be changed, what is the probability that a new oil filter is needed? (b) If a new oil filter is needed, what is the probability that the oil has to be changed?
Scores for a common standardized college aptitude test are normally distributed with a mean of 490 and a standard deviation of 103. Randomly selected students are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the preparation course has no effect.
If 1 student is randomly selected, find the probability that their score is at least 527.3.
P(X > 527.3) =
If 11 students are randomly selected, find the probability that their mean score is at least 527.3.
P(¯¯¯X > 527.3) =