Student loan debt is the only form of consumer debt that has grown since the peak of consumer debt in 2008. The average student loan of somebody younger than 30 is $22,350. Assume the standard deviation for debt is $8,000 per student. a. What is the probability that the sample mean will be less than $24,000 for a sample size of 40 students? b. Identify the symmetrical interval that includes 82% of the sample means if the true population mean is $22,350 per student. c. Answer the question in part a for a sample size of 80. Explain the differences between these two probabilities.
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!
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