1.a) If the true textbook cost is $524, what is the z-score and corresponding probability that you’d get a sample with a mean like the one we observed in Sample A or less? Provide an interpretation for your z-score. 1.b) Using this probability, does the reported value of $524 seem reasonable? 1.c) Should the administrators adjust the value? Justify your recommendation using the statistical support provided
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 Office of Financial Aid has historical data that indicates the standard deviation of textbook costs is steady from semester to semester at $287. Please use the info provided to answer the 3 subquestions:
1.a) If the true textbook cost is $524, what is the z-score and corresponding probability that you’d get a sample with a mean like the one we observed in Sample A or less? Provide an interpretation for your z-score.
1.b) Using this probability, does the reported value of $524 seem reasonable?
1.c) Should the administrators adjust the value? Justify your recommendation using the statistical support provided
Since, the question is not properly specified and does not provide a lot of information, the work is done on the basis of intuition, depending upon the information provided.
We see that, true text book cost is $524.
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