The distribution of the amount of money undergrads spend on books for a term is slightly right skewed, with a mean of $400 and a standard deviation of $80. A) If one student is selected at random, what is the probability that this student spends more than $425 on books?(show work) B) In a simple random sample of 100 undergrads what is the expected value of the sample mean amount of money spent on books?(show work) C) in a simple random sample of 100 undergrads, what is the standard deviation of the sample mean amount of money on books?
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 distribution of the amount of money undergrads spend on books for a term is slightly right skewed, with a mean of $400 and a standard deviation of $80.
A) If one student is selected at random, what is the probability that this student spends more than $425 on books?(show work)
B) In a simple random sample of 100 undergrads what is the
C) in a simple random sample of 100 undergrads, what is the standard deviation of the sample mean amount of money on books?(show work)
D) In a simple random sample of 100 undergrads, whats the probability that mean amount of money of 100 undergrads spent on books is between $400 and $500?
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