Question

If x is a binomial random variable, use the binomial probability table to find the probabilities below.

a.	P(x=4) for n=10, p=0.1	b..	P(x≤5) for n=15, p=0.5
c.	P(x>1) for n=5, p=0.3	d.	P(x<4) for n=15, p=0.7
e.	P(x≥18) for n=25, p=0.9.	f.	P(x=4) for n=20, p=0.2.

a P(x=4)=_____________________(Round to three decimal places as needed.)

b.P(x≤5)=_____________________(Round to three decimal places as needed.)

c P(x>1)=___________________(Round to three decimal places as needed.)

d.P(x<4)= ______________(Round to three decimal places as needed.)

e. P(x≥18)=_______________________ (Round to three decimal places as needed.)

f. P(x=4)_________________________equals=nothing(Round to three decimal places as needed.)

Answer 1

Given that, X is binomial random variable.

We want to find, the following probabilities using binomial probability table.

a) For n = 10 and p = 0.1

P(X = 4) = P(X ≤ 4) - P( X ≤ 3) = 0.998 - 0.987 = 0.011

P(X = 4) = 0.011

b) For n = 15 and p = 0.5

P(X ≤ 5) = 0.151

c) For n = 5 and p = 0.3

P(X > 1) = 1 - P(X ≤ 1) = 1 - 0.528 = 0.472

P(X > 1) = 0.472

d) For n = 15 and p = 0.7

P(X < 4) = P(X ≤ 3) = 0.000

e) For n = 25 and p = 0.9

P(X ≥ 18)

= 1 - P(X < 18)

= 1 - P(X ≤ 17)

= 1 - 0.002

= 0.998

P(X ≥ 18) = 0.998

f) For n = 20 and p = 0.2

P(X = 4) = P(X ≤ 4) - P(X ≤ 3) = 0.630 - 0.411 = 0.219

P(X = 4) = 0.219