Question
Asked Oct 17, 2019
If x is a binomial random variable, use the binomial probability table to find the probabilities below.
a. P(x<8) for n 15, p 0.7
b. P(x2 15) for n 25, p 0.3
c. P(x 2) for n 20, p 0.4
Click here to view a portion of the binomial probability table for n = 15.
Click here to view a portion of the binomial probability table for n = 20.
Click here to viewa portion of the binomial probability table for n 25
a. P(x 8)
(Round to three decimal places as needed.)
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If x is a binomial random variable, use the binomial probability table to find the probabilities below. a. P(x<8) for n 15, p 0.7 b. P(x2 15) for n 25, p 0.3 c. P(x 2) for n 20, p 0.4 Click here to view a portion of the binomial probability table for n = 15. Click here to view a portion of the binomial probability table for n = 20. Click here to viewa portion of the binomial probability table for n 25 a. P(x 8) (Round to three decimal places as needed.)

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Step 1

a.

The binomial probability table for n=15 and p=0.7.

From the binomial probability table for n=15 and p=0.7, we have

 

 

op
CUMULATIVE BINOMIAL PROBABILITIES
Tabulated values are P(< k)
(computations are rounded at the third decimal place.)
N 15
kp i
0.1
0.4
0.6
0.2
0.3
0.5
0.7
0.8
0.9
0
0.206 0.035 0.005
0.000 0.000 0.000 0.000 0.000 0.000
1
2
3
0. 549 0.167 0.035 0.005 0.000 0.000 0.000 0.000 0.000
0.816 0.398 0.127 0.027 0.004 0.000 0.000 0.000 0.000
0.944 0.648 0.297 0.091 0.018 0.002 0.000 0.000 0.000
0.987 0.836 0. 515 0.217 0.059 0.009 0.001 0.000 0.000
0.998 0.939 0.722 0.403 0.151 0.034 0.004 0.000 0.000
5
6
7
8
1.000 0.982 0.869 0.610 0.304 0.095 0.015 0.001 0.000
1.000 0.996 0.950 0.787 0. 500 0.213 0.050 0.004 0.000
1.000 0.999 0.985 0.905 0.696 0.390 0.131 0.018 0.000
1.000 1.000 0.996 0.966 0.849 0.597 .278 0.061 0.002
1.000 1.000 0.999 0.991i 0.941 0.783 0.485 0.164 0.013
10
1.000 1.000 1.000 0.998 0.982 0.909 0.703 0.352 0.056
1.000 1.000 1.000 1.000 0.996 0.973 0.873 0.602 0.184
1.000 1.000 1.000 1.000 1.000 0.995 0.965 0.8833 0.451
1.000 1.000 1.000 1.000 1.000 1.000 0.995 0.965 0.794
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
11
12
13
14
15
k: Number of success
p: Probability of success of one trial
P(X<8) P(XST)
0.050
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op CUMULATIVE BINOMIAL PROBABILITIES Tabulated values are P(< k) (computations are rounded at the third decimal place.) N 15 kp i 0.1 0.4 0.6 0.2 0.3 0.5 0.7 0.8 0.9 0 0.206 0.035 0.005 0.000 0.000 0.000 0.000 0.000 0.000 1 2 3 0. 549 0.167 0.035 0.005 0.000 0.000 0.000 0.000 0.000 0.816 0.398 0.127 0.027 0.004 0.000 0.000 0.000 0.000 0.944 0.648 0.297 0.091 0.018 0.002 0.000 0.000 0.000 0.987 0.836 0. 515 0.217 0.059 0.009 0.001 0.000 0.000 0.998 0.939 0.722 0.403 0.151 0.034 0.004 0.000 0.000 5 6 7 8 1.000 0.982 0.869 0.610 0.304 0.095 0.015 0.001 0.000 1.000 0.996 0.950 0.787 0. 500 0.213 0.050 0.004 0.000 1.000 0.999 0.985 0.905 0.696 0.390 0.131 0.018 0.000 1.000 1.000 0.996 0.966 0.849 0.597 .278 0.061 0.002 1.000 1.000 0.999 0.991i 0.941 0.783 0.485 0.164 0.013 10 1.000 1.000 1.000 0.998 0.982 0.909 0.703 0.352 0.056 1.000 1.000 1.000 1.000 0.996 0.973 0.873 0.602 0.184 1.000 1.000 1.000 1.000 1.000 0.995 0.965 0.8833 0.451 1.000 1.000 1.000 1.000 1.000 1.000 0.995 0.965 0.794 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 11 12 13 14 15 k: Number of success p: Probability of success of one trial P(X<8) P(XST) 0.050

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Step 2

b.

The binomial probability table for n=25 and p=0.3.

From the binomial pro...

CUNULATIVE BINOMIAL PROBABILITIES
Tabulated values are P(k)
(Computations are rounded at the third decimal place.)
N25
K\PI
.2
.7
o.1
o.3
o.4
o.5
o.6
o.8
o.072 0.004
o.000 0.000 0.000 0.000 0.000 0. 000 .000
o.271 .027 0.002 0.000 o.000 0. o00 0.000 o.000 0.000
.764 0.234 0.033 o.002 .000o o.000 0. 000 .000 .000
.902 .421 .090 o.009 .00o o.000 0.000 .000 .000
0.967 0.617 0.193 0.029 0.002 0.000 0.000 0.000 0.000
.991
o.998 0.891
o.780 0.341 0.074 0.007 0.000 0.o00 0.000 o.000
0.000 0.000 0.000
1.000 0.953 .677 o.274 0.054 0.004 0.000 .000 .000
1.000 0.983 0.811 o.425 0.11S o.013 0.000 0.000 o.000
.212 0.034 0.002 0.000 0.000
o. 512 0.154 0.022 o.001
1.000 0.994 0.902
0.S86
11
12
13
14
is
1.000 0.998 0.956 o.732 0.34s o.o7s 0.o06 0.000 o.000
1.000 1.000 0.983 0.846 O.300
1.000 1.00o o.994 0.922 0.655 0. 268 0.044 o.002 0.000
1.000 1.006 1.000 .987 .885 . 575 .189 o.017 .000
16
17
18
1.000 1.000 1.000 .996 0.946 0.726 0.323 o.047 .000
1.000 1.000 1.000 0.999
0.978
1.000 1.000 1.000 1.000 0.993
0.998
1.000 1.000 1.000 1.000 1.00o
0,846
o.926
.971
o.991
0.488
0.659
0.807
0.910 0.S79 0.098
0.109
o. 220 0.009
. 383 0.033
20
1.000 1.000 1.000 1.000 1.00o
.000 .000 1.000 i.000 1.000o 1.000 0. 991 0.902 o.463
i.000 .000o 1.000 1.000 1.000 1.000 0.998 o.973 0.729
1.000 1.000 1.000 1.000 1.000 1.000 1.000 o.996 0.928
1.000 .00o 1.000 1.000 1.000 1. 000 1.000 i.000 1.000
o.99 0.967
o.766 0.2136
23
P(X215) 1-P(X<14)
=1-0.998
0.002
NM D000 Nm
O0009
र्व क्व स्व स५
NNNNN
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CUNULATIVE BINOMIAL PROBABILITIES Tabulated values are P(k) (Computations are rounded at the third decimal place.) N25 K\PI .2 .7 o.1 o.3 o.4 o.5 o.6 o.8 o.072 0.004 o.000 0.000 0.000 0.000 0.000 0. 000 .000 o.271 .027 0.002 0.000 o.000 0. o00 0.000 o.000 0.000 .764 0.234 0.033 o.002 .000o o.000 0. 000 .000 .000 .902 .421 .090 o.009 .00o o.000 0.000 .000 .000 0.967 0.617 0.193 0.029 0.002 0.000 0.000 0.000 0.000 .991 o.998 0.891 o.780 0.341 0.074 0.007 0.000 0.o00 0.000 o.000 0.000 0.000 0.000 1.000 0.953 .677 o.274 0.054 0.004 0.000 .000 .000 1.000 0.983 0.811 o.425 0.11S o.013 0.000 0.000 o.000 .212 0.034 0.002 0.000 0.000 o. 512 0.154 0.022 o.001 1.000 0.994 0.902 0.S86 11 12 13 14 is 1.000 0.998 0.956 o.732 0.34s o.o7s 0.o06 0.000 o.000 1.000 1.000 0.983 0.846 O.300 1.000 1.00o o.994 0.922 0.655 0. 268 0.044 o.002 0.000 1.000 1.006 1.000 .987 .885 . 575 .189 o.017 .000 16 17 18 1.000 1.000 1.000 .996 0.946 0.726 0.323 o.047 .000 1.000 1.000 1.000 0.999 0.978 1.000 1.000 1.000 1.000 0.993 0.998 1.000 1.000 1.000 1.000 1.00o 0,846 o.926 .971 o.991 0.488 0.659 0.807 0.910 0.S79 0.098 0.109 o. 220 0.009 . 383 0.033 20 1.000 1.000 1.000 1.000 1.00o .000 .000 1.000 i.000 1.000o 1.000 0. 991 0.902 o.463 i.000 .000o 1.000 1.000 1.000 1.000 0.998 o.973 0.729 1.000 1.000 1.000 1.000 1.000 1.000 1.000 o.996 0.928 1.000 .00o 1.000 1.000 1.000 1. 000 1.000 i.000 1.000 o.99 0.967 o.766 0.2136 23 P(X215) 1-P(X<14) =1-0.998 0.002 NM D000 Nm O0009 र्व क्व स्व स५ NNNNN

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