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Collaborative statistics The normal distribution Review
The next two questions refer to:
X ~
U
(
3
,
13
)
Explain which of the following are false and which are true.
a
f
(
x
)
=
1
10
size 12{f \( x \) = { {1} over {"10"} } } {} ,
3
≤
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
)
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 Got questions? Get instant answers now!
Calculate:
a Mean
b Median
c 65th percentile.
a 8
b 8
c
P
(
x
<
k
)
=
0
.
65
=
(
k
−
3
)
∗
(
1
10
)
size 12{P \( x<k \) =0 "." "65"= \( k - 3 \) * \( { {1} over {"10"} } \) } {} .
k
=
9
.
5
size 12{k=9 "." 5} {} Got questions? Get instant answers now!
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 –
3
4
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 Got questions? Get instant answers now!
If
P
(
G
∣
H
)
=
P
(
G
)
size 12{P \( G \lline H \) =P \( G \) } {} , then which of the following is correct?
A
G
size 12{G} {} and
H
size 12{H} {} are mutually exclusive events.
B
P
(
G
)
=
P
(
H
)
size 12{P \( G \) =P \( H \) } {}
C Knowing that
H
size 12{H} {} has occurred will affect the chance that
G
size 12{G} {} will happen.
D
G
size 12{G} {} and
H
size 12{H} {} are independent events.
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If
P
(
J
)
=
0
.
3
size 12{P \( J \) =0 "." 3} {} ,
P
(
K
)
=
0
.
6
size 12{P \( K \) =0 "." 6} {} , and
J
size 12{J} {} and
K
size 12{K} {} are independent events, then explain which are correct and which are incorrect.
A
P
(
J
and
K
)
=
0
B
P
(
J
or
K
)
=
0.9
C
P
(
J
or
K
)
=
0.72
D
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). Got questions? Get instant answers now!
On average, 5 students from each high school class get full scholarships to 4-year colleges. Assume that most high school classes have about 500 students.
X = the number of students from a high school class that get full scholarships to 4-year school. Which of the following is the distribution of
X ?
A P(5)
B B(500,5)
C Exp(1/5)
D N(5, (0.01)(0.99)/500)
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Source:
OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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