The number of minutes of playing time of a certain high school basketball player in a randomly chosen game is a random variable whose probability density function is given in the following figure:
Find the probability that the player plays
(a) more than minutes;
(b) between minutes;
(c) less than minutes;
(d) more than minutes
(a) The probability that the player plays more than minutes is
(b) The probability that the player plays between is
(c) The probability that the player plays less than minutes is
(d) The probability that the player plays more than minutes is
Formalize the given probability function. As may be observed from the graph,
is the random variable with the density function defined . The needed probabilities are calculated as the integrals of the density function over the relevant intervals.
The annual rainfall in Cleveland, Ohio, is approximately a normal random variable with mean 40.2 inches and standard deviation 8.4 inches. What is the probability that (a) next year’s rainfall will exceed 44 inches? (b) the yearly rainfalls in exactly 3 of the next 7 years will exceed 44 inches? Assume that if Ai is the event that the rainfall exceeds 44 inches in year i (from now), then the events Ai, i Ú 1, are independent.
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