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You may need to use the appropriate appendix table or technology to answer this question. Consider a binomial experiment with

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Answer #1

Solution

given : n = 20, p= 0.70

Use Binomial formula "=BINOM.DIST(x, n, p,FALSE)" to find the probability

x Excel formula P(X=x) [Rounded to 4 decimal places]
0 =BINOM.DIST(0, 20, 0.70,FALSE) 0.0000
1 =BINOM.DIST(1, 20, 0.70,FALSE) 0.0000
2 =BINOM.DIST(2, 20, 0.70,FALSE) 0.0000
3 =BINOM.DIST(3, 20, 0.70,FALSE) 0.0000
4 =BINOM.DIST(4, 20, 0.70,FALSE) 0.0000
5 =BINOM.DIST(5, 20, 0.70,FALSE) 0.0000
6 =BINOM.DIST(6, 20, 0.70,FALSE) 0.0002
7 =BINOM.DIST(7, 20, 0.70,FALSE) 0.0010
8 =BINOM.DIST(8, 20, 0.70,FALSE) 0.0039
9 =BINOM.DIST(9, 20, 0.70,FALSE) 0.0120
10 =BINOM.DIST(10, 20, 0.70,FALSE) 0.0308
11 =BINOM.DIST(11, 20, 0.70,FALSE) 0.0654
12 =BINOM.DIST(12, 20, 0.70,FALSE) 0.1144
13 =BINOM.DIST(13, 20, 0.70,FALSE) 0.1643
14 =BINOM.DIST(14, 20, 0.70,FALSE) 0.1916
15 =BINOM.DIST(15, 20, 0.70,FALSE) 0.1789
16 =BINOM.DIST(16, 20, 0.70,FALSE) 0.1304
17 =BINOM.DIST(17, 20, 0.70,FALSE) 0.0716
18 =BINOM.DIST(18, 20, 0.70,FALSE) 0.0278
19 =BINOM.DIST(19, 20, 0.70,FALSE) 0.0068
20 =BINOM.DIST(20, 20, 0.70,FALSE) 0.0008

(a) f(12)=P(X = 12) = 0.1144

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(b) f(16) =PX = 16) = 0.1304

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(c) PX > 16) =?

PX > 16) =P(X = 16) + P(X = 17) + P(X = 18) +PX = 19) + P(X = 20

PX > 16) = 0.1304 +0.0716 +0.0278 +0.0068 + 0.0008

PX > 16) = 0.2375

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(d) P(X<15) =

PX<15)=P(X=0) + P(X = 1) + ........ +PX = 13) + P(X= 14)+PX = 15)

P(X<15) = 0.7625

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(e) E(X) = np = 20 * 0.7 = 14

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(f) Var(x) = np(1-P) = 20 * 0.7*(1 - 0.7) = 4.2

o= Var(x) = V4.2 = 2.0494

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