• Quiz 6.1 – 6.2 tomorrow
– May use both sides of one note card
• Test 6.1 – 6.2 on Monday
– May use both sides of one note card
Sections 6.1 and 6.2
Quiz tomorrow
Page 382, E21(a)
Regular die – Tetrahedral die
1
1
2
3
4
2
3
4
5
6
Page 382, E21(a)
1
1
0
2
1
3
2
4
3
5
4
6
5
2
-1
0
1
2
3
4
3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
Page 382, E21(a)
Shape of distribution?
Shape of distribution? Symmetric
Verify this is a probability
distribution.
Page 382, E22(a)
Page 382, E22(a)
-
1
1
0
2
2
0
3
3
0
4
4
0
5
5
0
6
6
0
Page 382, E22(a)
An oil exploration firm is to drill ten wells,
each in a different location. Each well has
a probability of 0.1 of producing oil. It will
cost the firm $60,000 to drill each well. A
successful well will bring in oil worth $1
million.
Taking into account the cost of drilling, what
is the firm’s expected gain?
An oil exploration firm is to drill ten wells,
each in a different location. Each well has
a probability of 0.1 of producing oil. It will
cost the firm $60,000 to drill each well. A
successful well will bring in oil worth $1
million.
a) E(gain) = 1,000,000(10)(0.1) – 60,000(10)
= $400,000
Page 379, E1
Page 379, E1
• Enter data for “Score” in list 1 and
“Proportion of Students” in list 2.
• Then, use 1-Var Stats L1, L2
Page 379, E1(a)
 x = 2.16
 x  2.2214
Page 379, E1(b)
Page 379, E1(b)
Sample of size 4
Page 379, E1(b)
Find the mean score for the sample of
size 4.
Page 379, E1(b)
Find the mean score for the sample of
size 4.
3
Page 392, E30(a)
Page 392, E30(a)
P(at least one works correctly)
= 1 – P(none work correctly)
= 1 – binompdf(2, .92, 0) = 0.9936
Page 392, E30(a)
P(at least one works correctly)
= 1 – P(none work correctly)
= 1 – binompdf(2, .92, 0) = 0.9936
or
Note: P(failure) is 0.08, so
P(at least one works correctly) =
1 – (0.08)2 = 0.9936
Page 392, E30(b)
Page 392, E30(b)
P(at least one works correctly)
= 1 – P(none work correctly)
= 1 – binompdf(3, .92, 0) = 0.9995
or
Note: P(failure) is 0.08, so
P(at least one works correctly) =
1 – (0.08)3 = 0.9995
What can cause two events to be
independent?
What can cause two events to be
independent?
(1) sampling with replacement
(2)
What can cause two events to be
independent?
(1) sampling with replacement
(2) small sample from a large population
What criteria must be met in order to have a
probability distribution?
What criteria must be met in order to have a
probability distribution?
(1) must include all possible outcomes
(2) probabilities sum up to 1
(3) no negative probabilities
When is it appropriate to use the normal
approximation to estimate the probability
for a binomial situation?
When is it appropriate to use the normal
approximation to estimate the probability
for a binomial situation?
Only if both of these are true:
np ≥ 10
n(1 – p) ≥ 10
If it is appropriate to use the normal
approximation to estimate the probability
for a binomial situation how do you
determine the expected value and the
standard deviation?
If it is appropriate to use the normal
approximation to estimate the probability
for a binomial situation how do you
determine the expected value and the
standard deviation?
E(X) = μx = np
If it is appropriate to use the normal
approximation to estimate the probability
for a binomial situation how do you
determine the expected value and the
standard deviation?
E(X) = μx = np
σx =
np(1  p)
If it is appropriate to use the normal
approximation to estimate the probability
for a binomial situation, then to find the
probability we can use:
normalcdf(left bound, right bound, mean,
standard deviation)
If it is appropriate to use the normal
approximation to estimate the probability
for a binomial situation, then to find the
probability we can use:
normalcdf(left bound, right bound, mean,
standard deviation)
normalcdf(left bound, right bound, np,
np(1  p) )
Suppose you flip a coin 13 times.
(1) what is the probability that you’ll get
exactly 7 heads?
(2) what is the probability that you’ll get at
least 7 heads?
(3) what is the probability that you’ll get at
most 7 heads?
Suppose you flip a coin 13 times.
(1) what is the probability that you’ll get
exactly 7 heads?
binompdf(13, 0.5, 7) = 0.2095
(2) what is the probability that you’ll get at
least 7 heads?
(3) what is the probability that you’ll get at
most 7 heads?
Suppose you flip a coin 13 times.
(2) what is the probability that you’ll get at
least 7 heads?
1 – binomcdf(13,0.5, 6) = 0.5
(3) what is the probability that you’ll get at
most 7 heads?
Suppose you flip a coin 13 times.
(2) what is the probability that you’ll get at
least 7 heads?
1 – binomcdf(13,0.5, 6) = 0.5
(3) what is the probability that you’ll get at
most 7 heads?
binomcdf(13, 0.5, 7) = 0.7095
When you spin a coin, the probability of
getting heads is 0.4. Suppose you take a
random sample of 5 spins. Construct the
probability distribution of the random
variable, X, defined as the number of
heads in your sample.
Number of heads in sample
P(x)
Number of heads in sample
0
1
2
3
4
5
P(x)
binompdf(5, 0.4)
Number of heads in sample
0
1
2
3
4
5
P(x)
0.0778
0.2592
0.3456
0.2304
0.0768
0.0102
Questions?
• Quiz 6.1 – 6.2 tomorrow
– May use both sides of one note card
• Test 6.1 – 6.2 on Monday
– May use both sides of one note card
Suppose you select five numbers at random
from 10 through 99, with repeats allowed.
Find the probability exactly three of the
numbers are even.
Suppose you select five numbers at random
from 10 through 99, with repeats allowed.
Find the probability exactly three of the
numbers are even.
P(even) = 0.5
Suppose you select five numbers at random
from 10 through 99, with repeats allowed.
Find the probability exactly three of the
numbers are even.
P(even) = 0.5
P(X = 3) = binompdf(5, 0.5, 3) = 0.3125
Suppose you select five numbers at random
from 10 through 99, with repeats allowed.
Find the probability exactly one of the
numbers has digits that sum to a number
greater than or equal to 9.
Suppose you select five numbers at random
from 10 through 99, with repeats allowed.
Find the probability exactly one of the
numbers has digits that sum to a number
greater than or equal to 9.
54
P(sum greater than or equal to 9) = 90 = 0.6
Suppose you select five numbers at random
from 10 through 99, with repeats allowed.
Find the probability exactly one of the
numbers has digits that sum to a number
greater than or equal to 9.
P(X = 1) = binompdf(5, .6, 1)  0.0768
Suppose you select five numbers at random
from 10 through 99, with repeats allowed.
Find the probability at least one of the
numbers has digits that sum to a number
greater than or equal to 9.
Suppose you select five numbers at random
from 10 through 99, with repeats allowed.
Find the probability at least one of the
numbers has digits that sum to a number
greater than or equal to 9.
P(X = at least 1) = 1 – P(X = 0)
= 1 – binompdf(5, .6, 0)
 0.9898