Jeopardy
Binom
Geom/
Expect
Norm
Q $100
Q $100
Q $100
Q $100
Q $200
Q $200
Q $200
Q $200
Q $200
Q $300
Q $300
Q $300
Q $300
Q $300
Q $300
Q $400
Q $400
Q $400
Q $400
Q $400
Q $400
Q $500
Q $500
Q $500
Q $500
Q $500
Q $500
Prob.
Dist.
Linear
Comb
Density
Curves
Q $100
Q $100
Q $200
Final Jeopardy
$100 Question from Prob. Dist
What is the probability when x=3?
x
P(x)
0
1
2
0.28
0.14
0.13
3
4
0.24
$100 Answer from Prob Dist
1 - (.28+.14+.13+.24)
1 - .79
.21
$200 Question from Prob Dist
x
P(x)
0
1
2
3
4
5
0.04
0.06
0.22
0.28
0.24
0.16
What is the P(x > 2)?
$200 Answer from Prob Dist
P(x > 2) = P(3) + P(4) +P(5)
= .28 + .24 + .16
= 0.68
$300 Question from Prob Dist
x
P(x)
0
1
2
3
4
5
0.04
0.06
0.22
0.28
0.24
0.16
Find the mean & standard deviation
$300 Answer from Prob Dist
Mean   x  p( x )
Mean  3.1
St . Dev 
x  
St . Dev  1.3
2
 p( x )
$400 Question from Prob Dist
x
P(x)
0
1
2
3
4
5
0.03
0.07
0.23
0.33
0.24
0.1
Find the probability that x is
within 2 deviations of the
mean.
$400 Answer from Prob Dist
Mean = 2.98
St. Dev. = 1.19
Mean±2Dev
2.98 ± 2(1.19)
0.6 to 5.36
Answer: 0.97
$500 Question from Prob Dist
x
P(x)
0
1
2
3
4
5
0.33
0.27
0.18
0.12
0.06
0.04
The distribution above represents the number of
broken eggs in a carton. What is the probability
that I randomly choose two cartons and exactly
the both have exactly ten unbroken eggs?
$500 Answer from Prob Dist
Ten unbroken = 2 broken
P(X=2 and x=2) = 0.18 * 0.18 = 0.0324
$100 Question from Linear Comb
Mean
St. Dev
A
14
3
B
22
4
Find:
3 x  4 y 5
$100 Answer from Linear Comb
3(14)+4(22)+5 = 135
$200 Question from Lin Comb
Mean
St. Dev
A
14
3
B
22
4
Find:
 2 x 3 y 8
$200 Answer from H2
Answer:
 2  3   3  4 
2
2
 180  3.416
$300 Question from Lin Comb
The following are the mean times and standard
deviations for the runners on a relay race team. Find
the mean time for the race and the standard deviation.
Ed
Mary
Ted
Julie
Mean
1.1
1.5
1.4
1.3
St. Dev
0.2
0.3
0.1
0.15
$300 Answer from Lin Comb
Answer:
Mean  1.1  1.5  1.4  1.3  5.3
St . Dev  .2  .3  .1  .15  0.1625  0.403
2
2
2
2
$400 Question from Lin Comb
The following represents the number of hours of work per doll
and number of dolls that Mary makes. She gets paid $4 per hour
and $20 per doll and there is a flat cost of $50 for supplies. Find
the average amount of money that Mary makes and the standard
deviation.
x = #hours
2
4
6
8
10
P(x)
0.14
0.18
0.22
0.25
0.21
y = #dolls
P(y)
4
0.12
7
0.14
10
0.28
12
0.32
15
0.14
$400 Answer from Lin Comb
Mean: 4(6.42)+20(10.2) – 50 = $179.68
St. Dev:
 4  2.673   20  3.212 
2
2
 4241.096  65.124
$500 Question from Lin Comb
The mean annual salary of employees
at a company is $36,000 with a
variance of $15,202,201. At the end
of the year, each employee receives a
$2000 bonus and a 4% raise (based on
salary). What is the mean and
standard deviation of the new
salaries?
$500 Answer from H2
Mean:
1.04(36000 )  2000  $39 , 440
St. Dev:
1.04  3899 
2
 16442700.6  $4054.96
$100 Question from Density
2
Find P(x < 6)
18
$100 Answer from Density
A=bh
1=16h
0.0625=h
A = 0.0625 * 4
A = 0.25
$200 Question from Density
16
Find the height.
$200 Answer from H3
A=1/2 bh
1=1/2 ( 16)h
1=8h
0.125 = h
$300 Question from Density
20
Find P(X < 6)
$300 Answer from Density
1=.5(20)H
1=10H
0.1 = H
14
h

20 0.1
20h  1.4
h  0.07
1
A  1  14  0.07 
2
A  1  0.49
A  0.51
$400 Question from Density
40
Find P(x < 7)
$400 Answer from Density
1
1   40  H
2
1  20 H
0.05  H
7
h

20 0.05
20h  0.35
h  0.0175
1
A   7  0.0175 
2
A  0.06125
$500 Question from Density
20
Find P(x < 18)
$500 Answer from Density
1
1   20  H
2
1  10 H
0. 1  H
2
h

10 0.1
10h  0.2
1
A  1   2  0.02 
2
A  1  .02
A  0.98
h  0.02
$100 Question from Binomial
In a recent survey they found that 25% of
U.S. adults prefer texting because “it’s
great for flirting.” In a sample of 50, what
is the mean & standard deviation of the
number who prefer texting due to the ease
of flirting
$100 Answer from Binomial
Mean:
St. Dev:
50( 0.25)  12.5
50(.25)(.75)  9.375  3.06
$200 Question from Binomial
A survey found that 41% of women in
the U.S. consider reading their favorite
leisure-time activity. If I randomly
select 12 women, find the probability
that exactly 7 consider reading their
favorite leisure-time activity. (Use
formula)
$200 Answer from Binomial
 12 
7
5
P( x  7 )     0.41  .59   0.1103
7 
$300 Question from Binomial
A survey found that 72% of people in
the U.S. prefer having a dog as a pet
than a cat. What is the probability
that in a sample of 82 people, less
than 57 prefer a dog? (Use calculator)
$300 Answer from Binomial
P(x < 57) = binomcdf (82, 0.72, 56)
= 0.2626
$400 Question from Binom
A survey found that 72% of people in
the U.S. prefer having a dog as a pet
than a cat. What is the probability
that in a sample of 59 people at least
40 prefer a dog? (Use calculator)
$400 Answer from Binom
P(x 40) = 1 – binomcdf (59, 0.72, 39)
= 1 – 0.1923
= 0.8077
$500 Question from Binom
Suppose we have a random
variable X where the probability
associated with the value k is
 12 
k
12  k
   .22   .78 
k 
For k = 0, 1, 2,….12. What is the
mean of X?
$500 Answer from Binomial
Mean = 12 (0.22) = 2.64
$100 Question from Geometric
The probability that a student passes the
written test for a private pilot’s license
is 0.68. what is the probability that a
student will not pass until the third
attempt?
$100 Answer from Geometric
P(x=3) = 0.322 *0.68 = 0.0696
$200 Question from Geometric
29% of American teens say that they
would break up with their
boyfriend/girlfriend for $10,000.
What is the probability that while
interviewing teens, you find one that
agrees within the first three asked?
$200 Answer from Geometric
P(x  3) = .29 + (.71*.29) + (.712*.29)
= .29 + .2059 + 0.1462
= 0.6421
$300 Question from Geometric
A glass manufacturer finds that 1 in
every 500 glass items produced is
warped. Find the probability that
the first warped glass item is in the
first four checked.
$300 Answer from Geometric
P(x  4)
= .002 + (.998*.002)+(.9982 *.002) + (.9983*.002)
= .002 + .001996 + .001992 + .00199
= 0.00798
$400 Question from Geometric
A basketball player has a 74% chance of
making a free throw. Find the
probability that the first free throw shot
he makes is on the third or fourth
attempt.
$400 Answer from Geometric
P(x=3 or x=4) = (.262*.74) + (.263*.74)
= 0.0500 + 0.0130
= 0.0630
$500 Question from Geometric
Two dice are rolled. If you roll a sum of 12
you can win $100. You can win $50 for a
sum of 10 or $5 for a sum of 8. If it costs
$10 to play this game, find the expectation
of the game.
$500 Answer from H5
 1 
 3   5 
E ( x )  100    50    5    10
 36 
 36   36 
 100 150 25 


   10
 36 36 36 
 275 

 10

 36 
 7.64  10
 2.36
$100 Question from Normal
The mean annual consumption of
peanuts are normally distributed with a
mean of 5.9 pounds per person and a
standard deviation of 1.8 pounds per
person. What percent of people annually
consume less than 4.5 pounds of peanuts
per person?
$100 Answer from Normal
P ( x  4.5) 
4 . 5  5 .9 

P z 
 P  z  0.78   0.2177

1 .8 

$200 Question from Normal
The thicknesses of washers produced by a
machine are normally distributed, with a
mean of 0.425 inch and a standard
deviation of 0.005 inch. A washer is
selected at random, find the probability that
the washer is between 0.423 and 0.426 inch
thick?
$200 Answer from Normal
P(0.423  x  0.426)
0.426  0.425 
 0.423  0.425
P
z

0.005
0.005


P   0 . 4  z  0 .2 
0.5793  0.3446
0.2347
$300 Question from Normal
The braking distances of a sample of
Nissan Altimas are normally distributed
with a mean of 129 feet and a standard
deviation of 5.18 ft. What is the longest
braking distance one of these Nissan
Altimas could have and still be in the
bottom 5%?
$300 Answer from Normal
x  129
1.645 
5.18
x  129  8.52
x  120.48
$400 Question from H6
The average time spent sleeping (in
hours) for medical residents is
normally distributed with a mean of
6.1 hours and a standard deviation
of 1.02 hours. Between what two
values does the middle 40% of the
sleep times lie?
$400 Answer from Normal
x  6. 1
0.52 
1.02
x  6.1  .5304
x  6.1
0.52 
1.02
x  6.1  .5304
x  5.5696
x  6.6304
$500 Question from Normal
The mean of a standardized test is
100. If the 85th percentile score is
110, find the standard deviation of
the test.
$500 Answer from Normal
110  100
1.04 
s
1.04 s  10
x  9.615
Final Jeopardy
What are the major differences between
binomial and normal distributions?
Final Jeopardy Answer
Binomial – discrete with
fixed number of trials with
two possibilities
Normal – continuous data