After deducting grants based on need, the average cost to attend the University of SouthernCalifornia (USC) is $27,175 (u.S. news & World report, america’s Best Colleges,2009 ed.). Assume the population standard deviation is $7400. Suppose that a randomsample of 60 USC students will be taken from this population.a. What is the value of the standard error of the mean?b. What is the probability that the sample mean will be more than $27,175?c. What is the probability that the sample mean will be within $1000 of the populationmean?
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!
After deducting grants based on need, the average cost to attend the University of Southern
California (USC) is $27,175 (u.S. news & World report, america’s Best Colleges,
2009 ed.). Assume the population standard deviation is $7400. Suppose that a random
sample of 60 USC students will be taken from this population.
a. What is the value of the standard error of the
b. What is the probability that the sample mean will be more than $27,175?
c. What is the probability that the sample mean will be within $1000 of the population
mean?
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