Transcript Jeopardy(Ch8) Normal Distn

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8.1
Continuous
Probability
Distributions
8.2
Normal Distribution
8.3
Normal
Sampling
8.4
Normal
Approximation
VARIOUS
QUESTIONS
( It’s empty.)
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Continuous
Distribution
NORMAL
DISTRIBUTION
NORMAL
SAMPLING
NORMAL
APPROXIMATION
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Various
CATEGORY 1 - $100
Describe a real-life example
that could have a continuous
probability distribution.
CATEGORY 1 - $200
Identify possible distribution for the
following experiments.
a) Tossing a coin.
b) rolling a die
c) Dealing five cards from a standard deck
CATEGORY 1 - $300
Describe key features of a Normal
probability distribution.
CATEGORY 1 - $400
Describe key features of a BiModal
probability distribution.
CATEGORY 1 - $500
Describe the difference between a
skewed right and a skewed left
probability distribution.
CATEGORY 2 - $100
An electrician is testing the accuracy of
resistors that have nominal resistance of 15
Ω(ohms). She finds that the distribution of
resistances is approximately normal with a
mean of 15.08  and a standard deviation
of 1.52  . What is the probability that a
resistor selected randomly has:a) a resistance < 14 ohms
b) has a resistance >15 ohms
c) has resistance between 14.08ohms and
16.08 ohms.
CATEGORY 2 - $200
Students marks on a test were normally
distributed with a mean of 70 and a
standard deviation of 5.
a) What percent of the student obtained a
mark of above 86%?
b) What percent of students obtained a B
grade (70-80)?
c) Determine the mark under which 75%
of these students’ marks occur (this is
referred to as the 75 th percentile.)
CATEGORY 2 - $300
To avoid a complete shutdown of the
assembly line if a component fails, major
manufacturing companies operate on the
principle of preventative maintenance. The
lifetime of one component is normally
distributed with a mean of 325h and a
standard deviation of 20 h. How frequently
should the component be replaced so that
the probability of its failing during operation
is <0.01
CATEGORY 2 - $400
Giselle is 168 cm. tall. In her high
school, girls’ height are normally
distributed with a mean of 174cm
and a standard deviation of 6cm.
What is the probability that the first
boy Giselle meets at school
tomorrow will be taller than she is?
CATEGORY 2 - $500
To run without causing damage, diameters
of engine crankshafts for a certain car
model must fall between 223.92 mm and
224.08mm. Crankshaft diameters are
normally distributed, with a mean of
224mm and a standard deviation of
0.03mm. What percent of these
crankshafts are like to cause damage?
CATEGORY 3 - $100
The list below gives the number of patrons per day
over a 30-day period during July at a theatre.
127,126,125,132,128,122,156,172,183,171,160,140,
154,160,122,187,185,158,112,145,168,187,117,120
,171,171,156,163,168,162.
a)
Use a method of your choice to assess whether
these data are normally distributed. Explain your
conclusion.
b)
Find the mean and standard deviation of these
data.
c)
Determine the probability that a day selected
randomly from this sample had at least 160 patrons.
State and justify any assumptions you have made.
CATEGORY 3 - $200
Assume that the data are normally distributed.
Mickey Mantle played for the New York Yankees from
1951–1968.
The table below gives the number of home runs he hit
each year during that time.
13,23,21,27,37,52,34,42,31,40,54,30,15,35,19,23,22,18.
a)
Calculate the mean and standard deviation of these
data.
b)
Estimate the probability that in a particular season
Mickey Mantle will hit more than 46 home runs.
CATEGORY 3 - $300
What measures of a normal
population can be estimated
based on a sample from a
normal population?
CATEGORY 3 - $400
A company produces boxes of candy coated chocolate
pieces. The number of pieces in each box is assumed to
be normally distributed with a mean of 48 pieces and a
standard deviation of 4.3 pieces. Quality control will
reject any box with fewer than 44 pieces. Boxes with 55
or more pieces will result in exess costs to the company.
a) What is the probability that a box selected at random
contains exactly 50 pieces ?
b) What % of the production will be rejected by quality
control as containing too few pieces?
c) Each filling machine produces 130,000 boxes per
shift. How many of these will lie within the acceptable
range?
CATEGORY 3 - $500
The weekly demand for laser printer cartridges
at Office Oasis is normally distributed with a
mean of 350 cartridges and a standard
deviation of 10 cartridges. The store has a
policy of avoiding stockouts (having no product
on hand). The manager decides that she wants
the chance of a stockout in any given week to
be at most 5% . How many cartridges should
the store carry each week to meet this policy?
CATEGORY 4 - $100
When can the normal
distribution be used to
approximate the binomial
distribution?
CATEGORY 4 - $200
It is estimated that 15% of the Canadian
population, given a choice of musical
events, would choose a pop/rock concert.
a) If 35 Canadians are randomly
surveyed, what is the probability that at
least 5 of them will choose a pop/rock
concert?
b) Compare the results from the normal
approximation with the results from the
calculations using a binomial distribution.
CATEGORY 4 - $300
A manufacturer of toys recalled one of
its products when it was discovered
that 30% of the toys had a defective
part. In a shipment of 600 of these
toys, what is the probability that
fewer than 200 are defective?
CATEGORY 4 - $400
It is estimated that 89% of Canadian
women are 150 cm or taller. If a poll of
400 Canadian women is conducted, what is
the probability that more than 360 of them
are 150 cm or taller?
a) State whether a normal distribution
approximation is reasonable for this
binomial distribution situation.
b) Then, determine the indicated
probability.
CATEGORY 4 - $500
A computer- chip manufacturer
knows that 72% of the chips
produced are defective. Suppose
3000 chips are produced every
hour. What is the probability that :a) at least 800 chips are
acceptable?
b) exactly 800 chips are acceptable?
CATEGORY 5 - $100
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CATEGORY 5 - $500
CATEGORY 1 - $100
Answer
Answers will vary.
The height of Humans.
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CATEGORY 1 - $200
Answer
a) Discrete probability distribution.
b) Discrete probability distribution.
c) Discrete probability distribution.
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CATEGORY 1 - $300
Answer
• Unimodal.
• Symmetric.
• Mean = Median = Mode
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CATEGORY 1 - $400
Answer
•Two Modes.
•Mean = Median
•Mean = Median are between the modes
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CATEGORY 1 - $500
Answer
Skewed Left – Distribution is shifted to the right.
(Mean < Median < Mode)
Skewed Right – Distribution is shifted to the Left.
(Mean > Median > Mode)
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CATEGORY 2 - $100
Answer
a)23.87%
b) 52.10%
C) 48.8%
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CATEGORY 2 - $200
Answer
a)0.069%
b) 47.7%
c) 73.4%
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CATEGORY 2 - $300
Answer
278.47
days.
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CATEGORY 2 - $400
Answer
84%
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CATEGORY 2 - $500
Answer
1 – 0.9923
=0.00777
=0.77%
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CATEGORY 3 - $100
Answer
Data are normally distributed.
Explanations will vary, but students
should notice that much of the data is
clustered around the mean and quite
evenly distributed above and below the
mean.
b) 151.6; 23.31
c) 0.3673; Answers may vary, but
students should observe that the data are
discrete, so continuity correction must be
used.
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CATEGORY 3 - $200
Answer
a) 29.78; 11.94
b) 0.08
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CATEGORY 3 - $300
Answer
The sample mean, x , and
sample standard deviation, s,
provide estimates of the
underlying parameters,  and .
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CATEGORY 3 - $400
Answer
a)8.2%
b)14.7%
c)102,000 boxes.
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CATEGORY 3 - $500
Answer
367
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CATEGORY 4 - $100
Answer
The normal distribution
can be used to approximate
the binomial distribution as
long as np and nq are both
greater than 5.
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CATEGORY 4 - $200
Answer
a) 0.6387
b) normal approximation: 0.6387
binomial distribution: 0.6193
The results using a normal
approximation are accurate to the
nearest tenth.
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CATEGORY 4 - $300
Answer
96%
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CATEGORY 4 - $400
Answer
a) The normal distribution
approximation is reasonable.
b) 24% (approximately for both
normal approximation and
binomial distribution)
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CATEGORY 4 - $500
Answer
a)0.9507
b)0.0432
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CATEGORY 5 - $100
Answer
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CATEGORY 5 - $200
Answer
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CATEGORY 5 - $300
Answer
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CATEGORY 5 - $400
Answer
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CATEGORY 5 - $500
Answer
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FINAL
CATEGORY
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FINAL CATEGORY
INSERT FINAL QUESTION
(ANSWER) HERE
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FINAL CATEGORY
WHAT OR WHO IS THE
FINAL ANSWER?
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END OF GAME
Daily Doubles and
usage notes follow...
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Contestant 1
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Contestant 2
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JEOPARDY! Slide Show
Setup
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The font for the question & answer slides is “Enchanted;” a copy of this font in located in the “REAL
Jeopardy Template” folder or included in the “jeopardy_pc.zip” file. (This font will need to be
installed in the C:/WINDOWS/FONTS folder of the computer running the show.) In order to keep all
of the sounds and fonts together, copy the entire “REAL Jeopardy Template” folder or
“jeopardy_pc.zip” file.
To change the categories:
– 1. Go to the “Edit”menu and choose “Replace…”
– 2. In the Find box, type CATEGORY X (X being 1 through 5) (all caps).
– 3. In the Replace box, type the category in all caps (for example, PRESIDENTS).
– 4. Click Replace All…
To change the dollar values (for example to create Double Jeopardy):
– 1. Go to the “Edit” menu and choose “Replace…”
– 2. In the Find box, type $X (the dollar value you want to change).
– 3. In the Replace box, type the new dollar value (with $).
– 4. Click Replace All...
JEOPARDY! Slide Show
Setup continued
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To set up the Daily Double:
– 1. Choose which dollar value(s) to set as Daily Double (normally, Jeopardy has one Daily
Double, and Double Jeopardy has two).
– 2. Go to the Game Board slide (Slide 8), right click once on the dollar value for the appropriate
question, choose Hyperlink, and choose Edit Hyperlink.
– 3. In the Edit Hyperlink window, go to “Named location in file” and click “Browse…”
– 4. In the Hyperlink to Slide window, scroll down to the appropriate slide; Slides 64 and 65 are
regular Daily Doubles, Slide 66 is an Audio Daily Double, Slide 67 is a Video Daily Double.
Click “OK.”
– 5. Go to the Daily Double slide just linked to, and right click once on the answer arrow at the
bottom right, choose Hyperlink, and choose Edit Hyperlink.
– 6. In the Action Settings window, make sure the Hyperlink button (to the left of “Hyperlink”) is
selected, and in the select box underneath choose “Slide…”
– 7. In the Hyperlink to Slide window, scroll down to the appropriate question slide (the original
slide number of the question).
NOTE: Using the Audio and Video Daily Doubles requires adding audio or video/picture clips to the
question slides. If you are not familiar with doing this in PowerPoint, do not use those Daily Doubles.
Running the JEOPARDY!
Slide Show
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On the game board with the categories on top (Slide 8), click on the desired dollar value. (The first
game board is used only to blink in the dollar values like the show.)
The question slide will pop up; the slides are timed with an eight-second timer. At the end of the
timer, an alarm will chime.
ICONS:
– ? Go to the answer screen.
– House Go back to the game board.
– Right Arrow (on Daily Doubles) Go to the question screen.
– Right Arrow w/ Bar (on Game Board) Go to the Final Jeopardy category.
– Turned-up Arrow Reload question screen after incorrect guess.
– $ Go to the Scoreboard slide.
– Left Arrow (on Scoreboard) Go to the previous slide.