Normal Distribution: Review
1.6
2008/06/17 16:26:16 GMT-5
2008/08/15 12:02:37.296 GMT-5
Barbara
Illowsky
illowskybarbara@deanza.edu
Susan
Dean
deansusan@deanza.edu
Connexions
cnx@cnx.org
elementary
statistics
The next two questions refer to:
X
~
U
(
3
,
13
)
Explain which of the following are false and which are true.
- a f(x)=110 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
Calculate:
- a Mean
- b Median
- c 65th percentile.
- a 8
- b 8
- c P(X<k)=0.65=(k−3)∗(110) size 12{P \( X<k \) =0 "." "65"= \( k - 3 \) * \( { {1} over {"10"} } \) } {}.
k=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 –
34 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) 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.
D
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 size 12{P \( J} {} and
K)=0 size 12{K \) =0} {}
- B
P(J size 12{P \( J} {} or
K)=0.9 size 12{K \) =0 "." 9} {}
- C
P(J size 12{P \( J} {} or
K)=0.72 size 12{K \) =0 "." "72"} {}
- D
P
(
J
)
≠
P
(
J
∣
K
)
size 12{P \( J \) <> P \( J \lline K \) } {}
- A False –
J size 12{J} {} and
K size 12{K} {} are independent, so they are not mutually exclusive which would imply dependency
- B False
- C True – since
P(J size 12{P \( J} {} and
K)≠0 size 12{K \) <> 0} {}, then
P(J size 12{P \( J} {} or
K)<0.09 size 12{K \) <0 "." "09"} {}
- D False –
P(J size 12{P \( J} {} and
K)≠0 size 12{K \) <> 0} {} are independent which implies
P(J)=P(J∣K) size 12{P \( J \) =P \( J \lline K \) } {}
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?
- AP(5)
- BB(500,5)
- CExp(1/5)
- DN(5, (0.01)(0.99)/500)
A