Download test two take-home problems

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Mathematics 109 take-home test two problems
due Tuesday, November 29, 2011
please show any relevant work to get credit for each problem
1. Suppose that a test for a certain disease
• returns a positive result for 95% of people with the disease, and a negative result for
5% of the people with the disease
• returns a negative result for 80% of the people without the disease, and a positive result
for 20% of the people without the disease
Assuming that 20% of the population has the disease, compute the probability of
(a) a person with a positive test result actually having the disease
(b) a person with a negative test result actually not having the disease
2. Suppose in a certain city the heights of both young adult females & males are normally
distributed. The parameters for each population are
• females: mean µ = 168 cm and standard deviation σ = 5 cm
• males: mean µ = 173 cm and standard deviation σ = 6 cm
(a) what percentage of the females are taller than the male mean height?
(b) what percentage of the males are shorter than the female mean height?
(c) a randomly chosen female and male couple walk into a room. What is the probability
of the female being taller than the male mean height and the male being shorter than
the female mean height?
(d) a randomly chosen group of two males and two females walk into a restaurant. What
is the probability that both males are 175 cm or taller or both females are 166 cm or
shorter.
3. For your randomly chosen sample of 32 daily maximum temperatures (in ◦ F) of a certain
U.S. city (provided by the instructor),
(a) compute the sample’s mean and standard deviation
(b) construct 90%, 98%, and 99.9% confidence intervals for mean high temperature.
(c) compute the proportion of your temperatures which are 40 degrees or lower.
(d) construct 80%, 93%, and 98% confidence intervals for the proportion of temperatures
which are 40 degrees or lower.