Download summary along with some simple problem solved

Things that you should know before starting these exercises
1. X - N(p,o) refers to a random variable X with a
mean of p and a standard deviation of o.
-
N(3.1 , 1.23!.refers to a random variable X
whose mean is 3.1and whose standard deviation is 1.23.1
[Thus, X
,..the normal with mean=0 and standard deviation=1".
[That is, Z - N(0 , 1) ]
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3.
e
Z-scores are in standard deviations from 0 (the mean).
[For example,Z=L.5 means 1.5 standard deviations from 0 (the mean].1
I^:o t= 1.5 iS l,S sfq..&*^t &q*'rqf i*rr {rm^ $\* il.er^ (0)
4.
The standard normal table ALWAYS gives the area
under the normal curve to the left of the given z value.
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7
The area under a normal curve represents a
probability-
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,
(t^sn^g 9r* shdq"r
nsr#*\ 1"W*)
t=l
for example , PIZ < 1.2) is the probability that the standard
normal random variable Z is LESS THAN 1.2.
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t: l,I
So [email protected]{ l.})= St\9
,:- ttsg 7.
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6. To use the standard normaltable to calculate
a probability
for a GREATER THAN, you must use the fact that
P(Z > a) =
1-
P{Z <a}.
for example, P(Z > 1] = 1- P(Z < 1)
...and you can look up P(Z < 1) in the standard normal table.l
[So,
(, **'F* t^t'Q*, P(e'i)= O't't
lJ
So 7(z,l)= t - o,tYl3 : 0,rstl
7.
To calculate the probability that a standard normal random
variable is between two numbers, you {a} look up the larger
number in the standard normal table, (b) look up the smaller
number and (c) subtract the smaller number from the larger.
P(t';?s6)
f6Th: zLr "rb)=?(z:1,'d")
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o,ttcs
B.
-
o') I I*3 :O-t5
:
To calculate a probability related to a normal random
I
with mean p and standard deviation o
N(p, o] l, it must first be converted to a standard
variable
*
IX
ti
X
normal random variable Z using
, -f..
Once converted, thg probability is calculated
N ( 1$-?
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-
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(-t-4- L+(+\
=\ r(\:
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r( e,,L."*(
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lf you must find a z-score corresponding to a certain probability,
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z
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you have to find the number in the body of the standard normal
table that is closest to the given probability and then cross-
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Normal Distribution
Examples HoME
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Some simple problems to work in class (use table as needed):
1. Find the percent of area (round
to nearest percent) under the normal
curve
(a) between the mean and 0.35 standard deviations from the mean.
(b) between the mean and -0.35 standard deviations from the mean.
2. Find the percent of the total area under the standard normal curve
between the z-scores: z = -1.1 and z = 0.8.
3. Find the z-score such that 1 8% of the total area is to the (a) left and (b)
right of z.
4.P(-1.1 <Z<2.A1=7
5. lf X
- N(4.2,1.1),
(a) P(X < a)
(b) P(x > 5)
(clP(4<x<5)
calculate the following:
HOME
Some simple problems to work in class (use table as needed):
1. Find the percent of area {round to nearest percent) under the normal cun/e
N"k'. f*',s rnmsurej i"., :t*..tn,",[ dq{,rli.o.s
(a) between the mean and 0,Q€ standard deviations from the mean.
Su\-uq,Z=Olts
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o,ir)- F(a^.il
bd'"**. b { b,\5 =?(acTt
| r*
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::1"o" Soco
- = e"bt6t
e=os;*-*d*oq*t
=
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A
f G.\,
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=
t
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t
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t:o"E
lo"ky.;
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i^
si,i.
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= o.b5t1
Kr.it* G*t
13,6t %
n"f"l +o!l=
c.i
:
3
bKuqr.t
s1n p1fu;u
o"3C3a:
P(.1'.\)-P(t;i, l)
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2. Find the percent of the total area under the standard normal curve
scores: z= -1.1 and z = 0.8.
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I
nt"n*lc.urv(
P(q") - P(i.;o,ls)
h:1":11,. o,,
b*.*Y*,,..-4,3t
4O =
t:=(}-lt *:CI
7o
ir c ({5+ddn= t)
(b) between the mean and -0.35 standard deviations from the mean.
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A,39
o,
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39
35
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Z.= -?:
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Normal Distribution Examples
t-NEXrl
Some simple problems to work in class (use table as needed):
(trr irn-r!\*p !>* k""1,u'J5,*y}-.,i
\*1 k*ror', fiq t4ittq
N.4u :. &*", \r$ia *d.v*,l- r,+ ru-$ +',* $; *,J T\1* Z se,;rt T\r* {1'vripntqs $\"Ls Q i t c,.
3. Find the z-score such that 18o/o of the total area is to the (a) lefl
f$**
(r)
(t;
E=i
sr,*o;nr;F[t"t:
..$-+trqi,l,
t^Li*"
a..,& $,,r,$ F"e S t\or**t,t(ou,
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fru.'- A- gr'*Q'
tn!"lq+ -]lj n.lt\t
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t,1
( l*rsjt**
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t*
r;-ff**"*"
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4.P(-1.1 <Z<2.01=7
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f
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Normal Distribution Examples
Some simple problems to work in class (use table as
bI\
?=
vf
(a) P(X < 4)
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(b) P(x
'
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sl 1"!,&"5
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-+.)-\
(zaH3
?(x'i=TP(x.$ = \*?
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