Transcript Chapter 6 Review Olympics

Advanced Math Topics
Chapter 6 Review Olympics
• One sheet per player
• Make an answer column on the left hand side
of your sheet
• Work together to solve each question
• Winning team earns a reward
• We will go over the process and answers for
each
BRONZE
1 point
1) Find the missing probability.
x
0
1
2
3
4
p(x)
?
0.23
0.08
0.04
0.44
2) Find the mean of the probability
distribution.
x
0
1
2
3
4
5
6
p(x)
0.1
0.1
0.1
0.2
0.15
0.3
0.05
3) 45% of college applicants into the UC
system are accepted. If there are 200,000
applicants, how many can be expected to
be accepted? What is the standard deviation.
Round to the nearest hundredth.
4) If the variance of a probability distribution
is 3.457, what is the standard deviation?
Round to the nearest hundredth.
SILVER
2 points
5) Find the standard deviation to the
nearest hundredth.
x
0
1
2
3
4
5
6
p(x)
0.11
0.21
0.4
0.12
0.10
0.04
0.02
6) The probability that a customer at a gas
station purchases diesel is 0.15. If six drivers
pull into a gas station, find the probability
that exactly 2 of them purchase diesel. Round to the nearest
hundredth of a percent.
7) The number of particles emitted from
a radioactive source has an average of
4 particle per minute. Find the probability
that exactly 2 are emitted. Round to the nearest
hundredth of a percent.
8) A package of mixed nuts contains 20
walnuts and 80 almonds. Five are grabbed
in one handful. Find the probability that
exactly one is a walnut. Round to the nearest
hundredth of a percent.
GOLD
3 points
9) Men’s Wearhouse got a shipment of
90 suits. Eight of them are missing shoes.
You randomly grabbed 6 suits. Find the
probability that at least 5 have shoes. Round to the nearest
hundredth of a percent.
10) According to police statistics, only
71% of crimes go reported. If ten crimes
are randomly selected, find the probability
that at most 2 are not reported. Round to the nearest
hundredth of a percent.
• Rows 1 and 2 Trade Papers
• Rows 3 and 4 Trade Papers
• Rows 5 and 6 Trade Papers
• Score only one sheet, then add it to their
teammate’s score.
• Points: Gold = 3 Silver = 2 Bronze = 1
• If there is more than 1 part, all parts must be
correct to get the points
BRONZE
1 point
1) Find the missing probability.
x
0
1
2
3
4
p(x)
?
0.23
0.08
0.04
0.44
Process: The probabilities must add to 1.
Answer: 0.21
2) Find the mean of the probability
distribution.
x
0
1
2
3
4
5
6
p(x)
0.1
0.1
0.1
0.2
0.15
0.3
0.05
Process: Summate x times p(x).
Answer: 3.3
3) 45% of college applicants into the UC
system are accepted. If there are 200,000
applicants, how many can be expected to
be accepted? What is the standard deviation.
Round to the nearest hundredth.
Process: Multiply n(p) to find the average.
Multiply n(p)(q) and take the square root to find the
standard deviation.
Answer: 90,000
and 222.49
4) If the variance of a probability distribution
is 3.457, what is the standard deviation?
Round to the nearest hundredth.
Process: Square root the variance
Answer: 1.86
SILVER
2 points
5) Find the standard deviation to the nearest
hundredth.
x
0
1
2
3
4
5
6
p(x)
0.11
0.21
0.4
0.12
0.10
0.04
0.02
Answer: 1.36
Process: There are 2 methods. The more common method
is to summate x2•p(x) and then subtract μ2. Then, square
root.
6) The probability that a customer at a gas
station purchases diesel is 0.15. If six drivers
pull into a gas station, find the probability
that exactly 2 of them purchase diesel. Round to the nearest
hundredth of a percent.
Process: Since the probabilities are independent…
Use the binomial distribution formula.
2(0.85)4
C
(0.15)
6 2
Answer: 17.62%
7) The number of particles emitted from
a radioactive source has an average of
4 particle per minute. Find the probability
that exactly 2 are emitted. Round to the nearest
hundredth of a percent.
Process: Since there is an average over a given region
or period of time, use the Poisson formula.
Answer: 14.65%
8) A package of mixed nuts contains 20
walnuts and 80 almonds. Five are grabbed
in one handful. Find the probability that
exactly one is a walnut. Round to the nearest
hundredth of a percent.
Process: Since there is no replacement, use the
hypergeometric formula. (20 choose 1)(80 choose 4)
divided by (100 choose 5).
Answer: 42.01%
GOLD
3 points
9) Men’s Wearhouse got a shipment of
90 suits. Eight of them are missing shoes.
You randomly grabbed 6 suits. Find the
probability that at least 5 have shoes. Round to the nearest
hundredth of a percent.
Process: P(5 have shoes) + P(6) since you cannot choose
more than 6 with shoes. Since there is no replacement,
use the hypergeometric formula for P(5) and P(6).
Answer: 91.30%
10) According to police statistics, only
71% of crimes go reported. If ten crimes
are randomly selected, find the probability
that at most 2 are not reported. Round to the nearest
hundredth of a percent.
Process: Since the probabilities are independent…
Use the binomial distribution formula for p(0) + p(1) + p(2)
are not reported.
Answer: 40.99%
Tiebreaker) The probability of getting on the Wall
of Fame is 0.04. You randomly select
3 people from the class, find the probability
exactly one person made the Wall of Fame.
Say your answer as a percent rounded
to the nearest hundredth of a percent.
Answer:
11.06%
HW
• P. 347 #1-11 (Skip 4, 9, 10)
• To study, look at this slideshow, past
slideshows, the book, the chapter review,
etc.
• Winners: Odds
• Test Tomorrow