Question

In a binomial distribution, n=7 and π=.15. Find the probabilities of the following events. (Round your answers to 4 decimal places.)

(a) x=1

Probability=

(b) x≤2

Probability =

(c) x≥3

Probability=

Answer #1

X ~ Bin ( n , )

Where n = 7 , = 0.15

P(X) = ^{n}C_{x} *
^{x} * ( 1 -
)^{n-x}

a)

P(X = 1) = ^{7}C_{1} * 0.15^{1} * ( 1 -
0.15)^{6}

= **0.3960**

b)

P(X <= 2) = P(X = 0) + P(X = 1) + (X = 2)

= ^{7}C_{0} * 0.15^{0} * ( 1 -
0.15)^{7} +^{7}C_{1} * 0.15^{1} * (
1 - 0.15)^{6} +^{7}C_{2} * 0.15^{2}
* ( 1 - 0.15)^{5}

= **0.9262**

c)

P(X >= 3) = 1 - P(X <= 2)

= 1 - 0.9262

= **0.0738**

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