Download Econ 3000 - Missouri State University

Senior Seminar Assignment 1
Due January 31, 2007
1. From 1974 to early 2002, the DJIA returns .27% per week (i.e., from Monday’s open
to Friday’s close) with a variance of 4.36. Find the probability that the DJIA will return
more than 1% in any given week? Find the probability that the DJIA will have a negative
return for the week. Find the probability that the DJIA will return less than -1% in any
given week.
2. Scores on the Stanford-Binet IQ test are assumed to be normally distributed with a
mean of 100 and a standard deviation of 16. What percent of the population has an IQ
above 140? Below 70?
3. An important measurement in the textile industry in the tensile strength of a produced
material. Suppose that the tensile strength of a roll of woven polypropylene in normally
distributed with a mean of 89 and a variance of 16. What is the probability that the
tensile strength will be between 80 and 100? What is the probability that the tensile
strength will be between 95 and 100?
4. Suppose the mean account in an investment firm is $8,000 and the standard deviation
is $2,000. Assuming a normal distribution, what percent of the accounts have a balance
above $13,000? Below $9,000? Between $3,000 and $6,000?
5. Suppose that we have a normal distribution with a mean of 70 and a standard
deviation of 15. Find the value of b so that 80% of the probability lies below it. In other
words, if x is a normal random variable with a mean of 70 and a standard deviation of 15,
find b so that P(x < b) = .80