A recent study found that 27% of adults often purchase used items istead of new ones. Assume a random sample of 75 adults are chosen. a.) Describe the distribution of the variable p. I. Shape. You must justify (state how you know) your answer. II. Mean. III. Standard deviation. Express your answer to four decimal palces. b.) Find the probability that the percentage of adults out of 75 who often purchase used items is more than 30%. c.) Find the probability that he percentage of adults out of 75 who often purchase used items is between 28 and 32%.
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!
A recent study found that 27% of adults often purchase used items istead of new ones. Assume a random sample of 75 adults are chosen.
a.) Describe the distribution of the variable p.
I. Shape. You must justify (state how you know) your answer.
II. Mean.
III. Standard deviation. Express your answer to four decimal palces.
b.) Find the probability that the percentage of adults out of 75 who often purchase used items is more than 30%.
c.) Find the probability that he percentage of adults out of 75 who often purchase used items is between 28 and 32%.
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