Download final take-home problems

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Mathematics 109 take-home test final problems
due Tuesday, December 13, 2011
please show any relevant work to get credit for each problem
1. The average life-spans of vegetarian and meat-eating populations are compared. A
sample of 144 vegetarians had a mean life-span of 75 years, with a sample standard standard
deviation of 5 years, while a sample of 100 meat eaters had a mean life-span of 72 years,
with a sample standard deviation of 4 years.
The following claim is made:
The mean life-span of a vegetarian is at least one year more than the mean life-span of a
meat-eater.
Can this claim be made with at most a one percent chance of making an error?
2. For a normally distributed population with mean income $56,000 and standard deviation
$12,000,
• calculate the quartiles of the income distribution
• calculate the 96th percentile of this income distribution.
3. An electronic device has six identical parts, each of one which has a 10% chance of failing
each year. The electronic device will continue to function as long as at least two of the six
identical parts are working.
• what is the probability that the electronic device will work for at least one year?
• what is the probability that the electronic device will work for at least five years?
4. Given the data between time x (in minutes) and position y ( in miles )
x
y
0.00 1.00 2.00 3.00 4.00 5.00 6.00
1.44 2.43 3.14 4.79 6.99 6.67 7.76
• plot the data, and visually draw a best-fit line
• estimate an equation for the best-fit line from your graph
• calculate the (Pearson) correlation coefficient for this data.
• is this data linear (with less than a 5% chance of an error?)
• calculate the equation for the least-squares best-fit line.