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Mathematics 146 homework exercises
due Tuesday, November 27, 2012
1. During spring quarter 2012, a student received a grade of 3.7 in a five-credit course, 2.5
in a four-credit course, and a grade of 4.0 in a three-credit course. What was the student’s
grade point average spring quarter?
2. Weights in a distant population are normally distributed about a mean of 62 kilograms,
with a standard deviation of 4 kilograms. Calculate the weights that correspond to (a) the
10th percentile, (b) the first quartile, (c) the median, (d) the third quartile, and (e) the 99th
percentile.
3. A survey of 400 randomly selected people found that 27% hated eating fish of any kind.
Construct a 97% confidence interval for the percent of the population which hates eating
fish.
4. In the same large city where 27% of the people hate eating fish, it is also the case that
35% of the people actually love eating fish. If two of this city’s people are randomly selected,
what is the probability that one hates fish and the other loves fish?
5. During the first week of the quarter, the 35 people in our classroom had a mean age of
29.63 years, with a (sample) standard deviation of 10.79 years. Assuming that ages across
the college are normally distributed, construct a 90% confidence interval for the mean age
at the college.
6. A local pizza shop calculates that the probability of each customer getting exactly the
pizza they want is 98%. For the next ten thousand customers, calculate the probability that
at most 200 customers don’t get the pizza they want.
7. A sample of heights is drawn from a larger population in which heights are normally
distributed. The following heights were observed, along with the number of people with
each height:
height (cm) frequency
164
20
166
30
168
34
170
31
172
19
(a) calculate the sample’s mean height and the standard deviation of the heights.
(b) construct a 95% confidence interval for the entire population’s mean height.