Question

In the exercise, X is a binomial variable with n = 6 and p = 0.1. Compute the given probability. Check your answer using technology. HINT [See Example 2.] (Round your answer to five decimal places.) P(3 ≤ X ≤ 5)

Answer 1

A binomial distribution is where there are identical events with only two possible outcomes. The probabilty of success p is same for each event.

We have

therefore x = 0 ,1 ,2,3, 4,5,6

=

P(3 ≤ X ≤ 5) = That means X is strictly 3 - 5 inclusive

= P( X = 3) + P(X = 4) + P(X = 5)

=

= 0.01458 + 0.001215 + 0.00005

P(3 ≤ X ≤ 5) = 0.0158

Using the excel function 'binomdist(x,n,p,false)'  false for not cumulative can generate binomial values.

x	P(X =x)
0	0.531441
1	0.354294
2	0.098415
3	0.01458
4	0.001215
5	0.00005
6	0.000001
Total	1