The score on an exam from a certain MAT 112 class, X, is normally distributed with μ=81.2 and σ=10. NOTE: Assume for the sake of this problem that the score is a continuous variable. A score can thus take on any value on the continuum. (In real life, scores are often treated as if they were continuous values but are actually discrete in most cases.) (a) Write the event ''a score less than 69.2'' in terms of X: . (b) Find the probability of this event: (c) Find the probability that a randomly chosen score is greater than 88.7: . (d) Find the probability that a randomly chosen score is between 69.2 and 88.7:
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The score on an exam from a certain MAT 112 class, X, is
NOTE: Assume for the sake of this problem that the score is a continuous variable. A score can thus take on any value on the continuum. (In real life, scores are often treated as if they were continuous values but are actually discrete in most cases.)
(a) Write the
(b) Find the
(c) Find the probability that a randomly chosen score is greater than 88.7: .
(d) Find the probability that a randomly chosen score is between 69.2 and 88.7:
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