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 ,1.231refers to a random variable X
whose mean is 3.1and whose standard deviation is 1.23.1
[Thus, X
2.
/\
X
iu*
g:3,t
Z-scores refer to the standard normal distribution
...the normal with mean=0 and standard deviation=1.
[That is, Z - N(0 , 1] l
STfiNDA$
NA?-rnflL
i:T_*-e
Z-scores are in standaid deviations from 0 (the mean).
[For example,Z=L.S means 1.5 standard deviations from 0 (the mean).]
ln:o t= 1"5 is l.S gfh^.\,,J dtt'u\oJi,rv {.oor" {\" n's'^
4.
(t)
The standard normal table ALWAYS gives the area
under the normal curve to the left of the given z value.
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The area under a normal curve represents a probabilityfor example , P(7 < 1.2) is the probability that the standard
normal random variable Z is LESS THAN 1.2.
u,'t1\1
$t*-Vth)
So TQz l-D= st\q
.
t.:1,1
,,\
t[,\g 7.
:
6. To use the standard normal table to calculate
a probability
for a GREATER THAN, you must use the fact that
P(Z > a) =
1-
P(Z <a).
[So, for example, PIZ>
Il = 1-
P(Z < 1)
...and you can look up P(Z < 1) in the standard normal table,l
(u ur"-Fo +'-IQa,
I'(e'D= s-\T 13
5o P(z'D= t-.1 ,tLrlJ:0,1S\l
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.
ff:t
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ar
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To calculate a probability related to a normal random
Ll
t
variable X with mean p and standard deviation o
IX
*
N{p, o) ], it must first be converted to a standard
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,
=
T.
Once converted, the probability is
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9.
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(-J,S
\
lf you must find a z-score corresponding to a certain probability,
you have to find the number in the body of the standard normal
table that is closest to the given probability and then crossreference that number back to the correspondipg
value. .
)
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Find the percentage of area under a normal curve between the mean and the given n r*ber of
standard deviations from the mean. This problem can be solved using technology or the table for
the standard normal curve from your text.
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Find the percent of the total area under the standard normal curve between the following z-scores.
This problem can be solved using technology or the table for the standard normal curve from your
text.
z= -1.5 andz= -0.5
(Round to the nearbst whole percent
as*
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the table for the standard normal curve from your text.
20o/o
of the total area is to the left of z.
(Round to the nearest hundredth a:; neetied.)
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the table for the standard normal curve from your text.
?3o/o
of the total area is to the right of z.
(Round to the nearest ltltndredth as
neecleci.
)
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Suppose that the life expectancy of a certain
brand of nondefective light bulbs is normally
distributed, with a mean life of 1100 hr and a
standard deviation
of
150 hr'
30,000 of these bulbs are produced, how many
can be expected to last at least 1100 hr?
If
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Suppose that the life expectancy of a certarn
brand of nondefective light bulbs is normally
distributed, with a mean life of 1800 hr and a
standard deviation of 150 hr.
If
30,000 of these bulbs are produced, how many
can be expected to last less than 1995 hr?
Use the following hnks to view the Standard
Normal Distribution table.
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Suppose that the life expectancy of a certain
brand of nondefective light bulbs is normally
distributed, with a mean life of 1400 hr and a
standard deviation of 50 hr.
If
70,000 of these bulbs are produced, how many
1330 hr and 1465 hr?
will last befween
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Find the percerlt of all chickens haring rr-eights rRore than 116l s or less thatr 1350 g
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-{ jar of peanrn buner contains -f 57 e rrith a standrrd dertation of 1t}"1 g- Find rhe probabilin
that a 1ar crntains Inftre than 1f 5 g. Assume a n'rrmal distributipn- Use a r-srsre r*unded t':
l
decimal places.
F N (gs),lo,L)
P(x>vGi=Fe'q*P)
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ln nutriuon the recsffffiended da:lv allou'ance iRD-tl of a ritamin is a nrimber set bv the
gsl'ffrr$eflt ar a guide io afl indiridual's dailv ritamin intakn- -tcnrallv, ritamin needs 1.Er.r'
drasticallv frsm person to persorr- brrt the needs are rEr]- clasnlr' appraximated $ a nsrmal
cut.l'e- To calculate the RD-+* thr gor-ef,nffient iirst hnds the average need for ritaminr arnong
people in the population and then the sturdard deriatian- The RD-t is dehned as the mean plur
l-5 times rhe standard dertation. Find the recommended dailv allo'"r'aflce for a ritamin gir-en thi
600 rurits. and the standard dertati,rn ir -t3
51 units,
the meur is 8*0
600
\l'hat is the recorrrrnended
51
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Rl}fi= -)e?.5
?=1fl
The
ritamin?