Private nonprofit four-year colleges charge, on average, $26,498 per year in tuition and fees. The standard deviation is $6,756. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 27,504 per year. c. Find the 76th percentile for this distribution. $ (Round to the nearest dollar.)
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!
Private nonprofit four-year colleges charge, on average, $26,498 per year in tuition and fees. The standard deviation is $6,756. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 27,504 per year.
c. Find the 76th percentile for this distribution. $ (Round to the nearest dollar.)
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