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Amanda is a recent college graduate, and has just started her first job. She would like to
know if she saves $5,000 per year out of her salary over the next 30 years what the
distribution of the value of her retirement fund after 30 years. She has decided that she
will invest all her money in the stock market that she estimates has a return that is
normally distributed with mean 12% per year and standard deviation 25%.
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What is the standard deviation of the ending balance? What does the distribution look
like now? What should Amanda infer from this?
To form a scatterplot of X versus Y, X and Y must be paired
Lilliefors test for normality compare two cumulative distribution functions (cdf‘s): the
cdffrom a normal distribution and the cdfcorresponding to the given data (called the
empirical cdf).
A data set from a sample of 399 Michigan families was collected. The characteristics of
the data include family size (large or small), number of cars owned by family (1, 2, 3,
or 4), and whether family owns a foreign car. Excel produced the pivot table shown
below.
Use this pivot table to determine how family size and number of cars owned influence
the likelihood that a family owns a foreign car.
A good shipping plan uses as many cheap routes as possible, but ultimately is
constrained by capacities and demands.
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A sample of 1000 households was selected in Los Angeles to determine information
concerning consumer behavior. Among the questions asked was “Do you enjoy
shopping for clothing?” Of 480 males, 272 answered yes. Of 520 females, 448
answered yes.
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What is the probability that a respondent chosen at random is a male and does not enjoy
shopping for clothing?
In stratified sampling with proportional sample sizes, the proportion of each stratum
selected differs from stratum to stratum.
In aggregate planning models, the number of workers available influences the possible
production levels.
When we solve a linear programming problem with Solver, we cannot guarantee that
the solution obtained is an optimal solution.
If events A and B have nonzero probabilities, then they can be both independent and
mutually exclusive.
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Suppose that patrons of a restaurant were asked whether they preferred beer or whether
they preferred wine. 60% said that they preferred beer. 70% of the patrons were male.
80% of the males preferred beer.
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Are gender of patrons and drinking preference independent? Explain.
If the standard deviations of X and Y are 15.5 and 10.8, respectively, and the covariance
of X and Y is 128.8, then the coefficient of correlation r is approximately 0.77.
The cyclic component of a time series is more likely to exhibit business cycles that
record periods of economic recession and inflation.
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Suppose that patrons of a restaurant were asked whether they preferred beer or whether
they preferred wine. 60% said that they preferred beer. 70% of the patrons were male.
80% of the males preferred beer.
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Suppose a randomly selected patron is a female. What is the probability the patron
prefers beer?
In testing the overall fit of a multiple regression model in which there are three
explanatory variables, the null hypothesis is .
Proportionality, additivity, and divisibility are three important properties that LP models
possess, which distinguish them from general mathematical programming models:.
If the p-value is sufficiently small for an ANOVA test, we can that all the population
means are equal.