Question

​34% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles.

Required:
Construct a binomial distribution using n= 0.6 and p=0.34

Answer 1

solution below

Explanation:

The question says 6 working mother's were selected so n = 6 not 0.6

We are expected to find

P(X = 0,1,2,3,4,4,6)

1. When x = 0

6C0*(0.34)⁰*(0.66)⁶

= 1 *1* 0.827

= 0.0827

2. When X = 1

6C1*(0.34)¹*(0.66)⁵

= 6 x 0.34 x 0.252

= 0.2555

3. When X = 2

6C2*(0.34)²*(0.66)⁴

= 15 x 0.1156 x 0.1897

= 0.3289

4. When x = 3

6C3*(0.34)³*(0.66)³

20 x 0.039304 x 0.2875

= 0.2599

5. When X = 4

6C4*(0.34)⁴*(0.66)²

= 15 x 0.01336 x 0.4356

= 0.8729

6. When x = 5

6C5*(0.34)⁵*(0.66)¹

= 6 x 0.0045 x 0.66

= 0.01782

7. When x = 6

6C6*(0.34)⁶*(0.66)⁰

1 x 0.0015 x 1

= 0.0015