Statistics Questions
1.Blood cocaine concentration (mg/L) was determined both for
a sample of individuals who had died from cocaine-induced excited delirium (ED)
and for a sample of those who had died from a cocaine overdose without excited
delirium (non-ED); survival time for people in both groups was at most 6 hours.
The accompanying data comes from “Fatal Excited Delirium Following Cocaine
Use” (J. of Forensic Sciences, 1997: 25-31).
ED: 0.0, 0.0, 0.0, 0.0, 0.1, 0.1, 0.1, 0.1, 0.2, 0.2, 0.3,
0.3, 0.3, 0.4, 0.5, 0.7, 0.8, 1.0, 1.5, 2.7, 2.8, 3.5, 4.0, 8.9, 9.2, 11.7,
21.0.
Non-ED: 0.0, 0.0, 0.0, 0.0, 0.0, 0.1, 0.1, 0.1, 0.1, 0.2,
0.2, 0.2, 0.3, 0.3, 0.3, 0.4, 0.5, 0.5, 0.6, 0.8, 0.9, 1.0, 1.2, 1.4, 1.5, 1.7,
2.0, 3.2, 3.5, 4.1, 4.3, 4.8, 5.0, 5.6, 5.9, 6.0, 6.4, 7.9, 8.3, 8.7, 9.1, 9.6,
9.9, 11.0, 11.5, 12.2, 12.7, 14.0, 16.6, 17.8.
a. Construct a stem-and-leaf display for each data set.
b. Construct a box plot for each data set.
c. Compare the two displays with the two box plots, and draw
conclusions about the data.
2. A manufacturer of VCR’s purchases a particular microchip,
called the LS-24, from three suppliers: Hall Electronics, Schuller Sales, and
Crawford Components. Thirty percent of the LS-24 chips are purchased from Hall
Electronics, 20 percent from Schuller Sales, and the remaining 50 percent from
Crawford Components. The manufacturer has extensive histories on the three
suppliers and knows that 3 percent of the LS-24 chips from Hall Electronics are
defective, 5 percent of chips from Schuller Sales are defective, and 4 percent
of the chips purchased from Crawford Components are defective. When the LS-24
chips arrive at the manufacturer, they are placed directly in a bin and not
inspected or otherwise identified by supplier. A worker selects a chip for
installation in a VCR and finds it defective. What is the probability that it
was manufactured by Schuller Sales?
3. Five percent of the worm gears produced by an automatic,
high-speed Carter-Bell milling machine are defective.
a. Among ten randomly selected worm gears, how likely is it
that only one is defective?
b. Among ten randomly selected worm gears, what is the
probability that at least two are defective?
c. If the worm gears are examined one by one, what is the
probability that at most five must be selected to find four that are not
defective?
4. The amounts of money requested on home loan applications
at Easy Federal Savings and Loan Association follow a normal distribution, with
a mean of $320,611.00, and a standard deviation of $84,321.00. A loan
application is received this morning.
a. What is the probability that the amount requested is
$400,000.00 or more?
b. What is the probability that the amount requested is
between $300,000.00 and $350,500.00?
c. What is the middle symmetric range consisting of 90% of
the mortgages.?
5. An economist wishes to estimate the average family income
in a certain population. The population standard deviation is known to be
$4,500, and the economist uses a random sample of size = 225.
a. What is the probability that the sample mean will fall
within $800 of the population mean?
b. What is the probability that the sample mean will exceed
the population mean by more than $600.
6. The article “Reliability of Domestic Waste Biofilm
Reactors” (J. of Envir. Engr., 1995: 785-790) suggests that substrate
concentration (mg/cm^3) of influent to a reactor is normally distributed with
mu = 0.30 and sigma = 0.06.
a. What is the probability that the concentration exceeds
0.40?
b. What is the probability that the concentration is at most
0.25?
c. What is the 90th percentile of the substrate concentration
(i.e., the value that is exceeded by the largest 10% of all concentration
levels)?
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