Question

If ?x is a binomial random variable, compute ?(?) for each of the following cases:

(a) ?(?≤6),?=8,?=0.2

?(?)=

(b) ?(?>4),?=5,?=0.5

?(?)=

(c) ?(?<2),?=3,?=0.8

?(?)=

(d) ?(?≥5),?=9,?=0.6

?(?)=

Answer #1

Solution:

Here, we have to find the probabilities by using the binomial table.

(a) ?(?≤6),?=8,?=0.2

**?(****?≤6) =**
**0.999916**

[By using cumulative binomial table.]

(b) ?(?>4),?=5,?=0.5

?(?>4) = 1 - P(X≤4)

?(?>4) = 1 - 0.96875

[By using cumulative binomial table.]

**?(****?>4) =**
**0.03125**

(c) ?(?<2),?=3,?=0.8

?(?<2) = P(X≤1)

**?(****?<2) =**
**0.104**

[By using cumulative binomial table.]

(d) ?(?≥5),?=9,?=0.6

?(?≥5) = 1 - P(X<5)

?(?≥5) = 1 - P(X≤4)

?(?≥5) = 1 - 0.266568

[By using cumulative binomial table.]

**?(****?≥5) =** **0.733432**

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