The next two questions refer to:
X
X
~
U
(
3
,
13
)
U(3,13)
Explain which of the following are false and which are true.
- a: f(x)=110f(x)=110 size 12{f \( x \) = { {1} over {"10"} } } {},
3≤x≤133≤x≤13 size 12{3 <= x <= "13"} {}
- b: There is no mode.
- c: The median is less than the mean.
- d:
P
(
X
>
10
)
=
P
(
X
≤
6
)
P
(
X
>
10
)
=
P
(
X
≤
6
)
size 12{P \( X>"10" \) =P \( X <= 6 \) } {}
- a: True
- b: True
- c: False – the median and the mean are the same for this symmetric distribution
- d: True
Calculate:
- a: Mean
- b: Median
- c: 65th percentile.
- a: 8
- b: 8
- c: P(X<k)=0.65=(k−3)∗(110)P(X<k)=0.65=(k−3)∗(110) size 12{P \( X<k \) =0 "." "65"= \( k - 3 \) * \( { {1} over {"10"} } \) } {}.
k=9.5k=9.5 size 12{k=9 "." 5} {}
Which of the following is true for the above box plot?
- a: 25% of the data are at most 5.
- b: There is about the same amount of data from 4 – 5 as there is from 5 – 7.
- c: There are no data values of 3.
- d: 50% of the data are 4.
- a: False –
3434 size 12{ { {3} over {4} } } {} of the data are at most 5
- b: True – each quartile has 25% of the data
- c: False – that is unknown
- d: False – 50% of the data are 4 or less
If
P(G∣H)=P(G)P(G∣H)=P(G) size 12{P \( G \lline H \) =P \( G \) } {}, then which of the following is correct?
- A: GG size 12{G} {} and
HH size 12{H} {} are mutually exclusive events.
- B:
P
(
G
)
=
P
(
H
)
P
(
G
)
=
P
(
H
)
size 12{P \( G \) =P \( H \) } {}
- C: Knowing that
HH size 12{H} {} has occurred will affect the chance that
GG size 12{G} {} will happen.
- D: GG size 12{G} {} and
HH size 12{H} {} are independent events.
If
P(J)=0.3P(J)=0.3 size 12{P \( J \) =0 "." 3} {},
P(K)=0.6P(K)=0.6 size 12{P \( K \) =0 "." 6} {}, and
JJ size 12{J} {} and
KK size 12{K} {} are independent events, then explain which are correct and which are incorrect.
- A:
P(
J
and
K)P(
J
and
K)
=
0
=
0
- B:
P(
J
or
K)
=
0.9P(
J
or
K)
=
0.9
- C:
P(
J
or
K)
=
0.72P(
J
or
K)
=
0.72
- D:
P ( J )
≠
P (J
∣K)
P ( J )
≠
P (J
∣K)
- A:
False - J and K are independent so they are not mutually exclusive which would imply dependency (meaning P(J and K) is not 0).
- B:
False - see answer C.
- C:
True - P(J or K) = P(J) + P(K) - P(J and K)
= P(J) + P(K) - P(J)P(K)
= 0.3 + 0.6 - (0.3)(0.6) = 0.72.
Note that P(J and K) = P(J)P(K) because J and K are independent.
- D:
False - J and K are independent so P(J) = P(J|K).
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