Assignment
1. Scores on a particular test are normally distributed in the population, with a mean of
100 and a standard deviation of 15. What percentage of the population have scores ....
a) Between 100 and 125
b) Between 82 and 106
c) Between 110 and 132
d) Above 132
e) Equal to 132
2. Archeologists excavating at a Viking site in Newfoundland have determined that the
age of the artifacts they have discovered is normally distributed with a mean of 1000
years. Ninety-five percent of the artifacts are between 900 and 1100 years old.
a) What proportion of the artifacts are between 940 and 980 years old?
b) One archeologist is particularly interested in collecting the oldest 5% of the
artifacts. How old does an artifact have to be to fit in this collection?
c) The age of artifacts found at a neighbouring site is also normally distributed, with a
standard deviation of 60, but the artifacts at this second site are older, on average, than
those at the first site. In fact, only 33% of the artifacts at the first site are older than the
mean age of artifacts at the second site. What percentage of artifacts at the second site
are less than 1200 years old?
3. The population distribution of scores on a commonly used IQ test is normal with a
mean of 100 and a standard deviation of 15. The test was recently administered to a
sample of psychology undergraduates and to a sample of mildly depressed psychiatric
patients. Both groups yielded normally distributed IQ scores. The standard deviation
of the students' scores was 12 and that of the patients' was 17. The probability that a
psychology student has a lower IQ than the average person in the population was found
to be 10 percent. The probability that a patient has a higher IQ than the average
psychology student is 5 percent.
a) What is the probability that a randomly selected psychology student will have a
lower IQ than the average psychiatric patient?
b) What percentage of people from the general population will have a higher IQ than a
student at the 67th percentile of the psychology student distribution?
4. A supermarket manager finds that 20% of his customers buy brand X cornflakes. The
other 80% buy brand Z.
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