36% 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. Complete parts​ (a) through​ (c) below.a) contstruct a binomail distribution using n=6 and p=0.36x​P(x)0 1 2 3 4 5 6  b) graph the binomail distribution using a histogram and describe its shape.

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Asked Nov 26, 2019
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36% 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. Complete parts​ (a) through​ (c) below.
a) contstruct a binomail distribution using n=6 and p=0.36
x
​P(x)
0
 
1
 
2
 
3
 
4
 
5
 
6
 

 

b) graph the binomail distribution using a histogram and describe its shape.  

 

 

 
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Expert Answer

Step 1

A binomial distribution is used when an experiment has two possible outcomes, such as success and failures. The outcomes of the experiment should be independent of each other. 

For a binomial distribution with n independent trials, the probability of getting x successes among those n trials is defined as:

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P(Xx) "C, p (1-p) Here, "C, is the number of combinations of getting r successes in n trials. The probability of success of each trail is denoted by p

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Step 2

Given:

 n= 6 and p = 0.36

(a)

The binomial distribution table can be constructed as:

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P(X) C(0.36) x(1-0.36)0.069 1Cx(0.36 x(1-0.36) 0.232 2 ,x(0.36 x(1-0.36) 0.326 3x(0.36)x(1- 0.36)= 0.245 4C(0.36 (1-0.36)0.103 5C x(0.36 x(1-0.36) 0.023 6Cx(0.36) x(1-0.36)0.002 X 6-1 6-3 X X 6-6

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Step 3

Therefore...

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х Р(Х) 0 0.069 10.232 0.326 0.245 4 0.103 5 0.023 6 0.002

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