Download exercises due February 28th

name:
Mathematics 109 exercises
due Tuesday, February 28, 2012
please show any relevant work to get credit for each problem
2. 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 90% of the people without the disease, and a positive result
for 10% 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
3. Suppose in a certain city the heights of both young adult females are normally distributed
about a mean value of 170 centimeters. It is also known that 80% of the heights are within
6 centimeters of the mean.
(a) calculate the standard deviation for the heights
(b) estimate the first quartile for the heights
4. Suppose 32 data values are collected for gas prices:
• 7 of the prices were $3.45 a gallon
• 9 of the prices were $3.24 a gallon
• 16 of the prices were $3.52 a gallon
(a) compute the sample’s mean and standard deviation
(b) construct 90% confidence interval for the mean gas price per gallon
(c) estimate the sample size required to get a margin of error of $.02 for a 99% confidence
interval for the mean gas price per gallon.