Spring 2016 Math 166
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1. A manufacturing process produces
Week in Review VII
light bulbs with life expectancies
whicch are normally distributed with
a mean of 500 hours and a standard
deviation of 100 hours. What percentage of the light bulbs can be expected
to last between 380 and 560 hours?
courtesy: David J. Manuel
(covering Sections 3.2-3.4 and Exam II)
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Section 3.2-3.3
2. To the nearest hour, nd the range of
life for the middle 80% of light bulbs.
1. Thirty-two
employees of Megamonopoly Corporation were surveyed
about the number of hours (to the
nearest hour) spent commuting to and
from work each week, with the results
in the following table:
# of hours
Frequency
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3
4
2
5
6
Section 3.4
6
1
7
3
8
5
9
3
3. The life of a Turboboost Battery is nor-
10
4
11
3
Find the expected value, median,
mode, variance, and standard deviation for the data.
mally distributed with an average of
3.26 years and a standard deviation of
.19 years.
If the company oers a 3-year full re12
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placement warranty, what is the probability that they will have to replace
the battery?
2. Two fair 4-sided dice (#1-4) are tossed.
Let X = the dierence between the
4. If the company wants to replace at
most 1% of all batteries under their
warranty, how many years (to the nearest tenth) should the warranty last?
larger and smaller number. Find
E(X), the median, mode, V (X), and
the standard deviation.
3. Courtney Walker, an 80% free-throw
shooter, shoots 120 free throws during
the season. Let X = the number of 3
free throws made.
Exam II Review (2.1-3.1)
1. A box of 100 GPS systems from Mall-
wart contain 8 defective ones. A sample of nine are tested. Find the probability that at least one is defective.
(a) What is E(X)?
(b) What is V (X)?
(c) What is the standard deviation?
2. A phonelock password consists of 3 dig-
4. SquareTrade oers a 3-year extended
its (0-9).
warranty on a $600 Iphone for $86.29.
Ignoring depreciation, and assuming
the company anticipates at least breaking even on these warranties, what is
their calculated probability that the
Iphone will break over the next 3
years?
(a) How many passwords are possible if digits cannot be repeated?
(b) How many passwords are possible if digits can be repeated?
(c) How many passwords are possible if consecutive digits must be dierent?
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3. Forty pairs of identical twins apply for
9. Given the histogram below, if the three
a medical study.
missing bars have equal heights, nd
P (X ≥ 3).
(a) In how many ways can 6 pairs be chosen
for the study?
(b) After the 6 pairs are chosen, in how
many distinguishable ways can the 12
people line up for a publicity photo?
(c) In how many distinguishable ways can
the 12 line up for the photo if the twins
must stand next to each other?
0.3
0.1
? ?
1 2
6.
7.
8.
4
5
10. A Quidditch squad consists of 10 play-
4. Courtney Walker has an 80% free
5.
?
3
ers, including Harry and Ginny. A
team of seven is to be chosen at random to start. What is the probability
that Harry or Ginny are chosen?
throw percentage. She is fouled on a
3-point attempt and therefore gets to
shoot 3 free throws. Let X = the number of free throws she makes. Find a
probability distribution for X .
It is estimated that sixteen political
parties will have presidential candidates for the 2016 election. How many
ballots can be made each with the candidates in a dierent order on the ballot?
If one of the ballots is chosen at random, what is the probability that the
2 major party candidates (Republican
and Democrat) are listed rst (in any
order)?
Studies show that 60% of college students change their major. Of the
600 students registered for MATH 166,
what is the probability that at least
350 but no more than 400 of them will
change their major?
Six seniors and four juniors from the
Aggie Jenga Players club apply for ofcer positions for next semester.
(a) If a president and vice-president are chosen at random, what is the probability
that both are juniors?
(b) If a 3-person tournament committee is
to be formed from the applicants, what
is the probability that the majority will
be seniors?
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