Question 1193397
<font color=black size=3>
Answer: <font color=red>0.251722 (approximate)</font>


=========================================================================================================


Explanation:


x = number of successes = number of companies that send a representative
n = sample size = 20
p = probability a company sends a representative = 50% = 0.5


B(x) = binomial probability
B(x) = (n C x)*(p)^(x)*(1-p)^(n-x)
B(x) = (20 C x)*(0.5)^(x)*(1-0.5)^(20-x)
B(x) = (20 C x)*(0.5)^(x)*(0.5)^(20-x)
The n C x refers to the nCr combination formula.


Plug in x = 12
B(x) = (20 C x)*(0.5)^(x)*(0.5)^(20-x)
B(12) = (20 C 12)*(0.5)^(12)*(0.5)^(20-12)
B(12) = (125,970)*(0.5)^(12)*(0.5)^(8)
B(12) = 0.120134 approximately
This is the approximate probability exactly twelve companies send a representative.


Repeat for x = 13
B(x) = (20 C x)*(0.5)^(x)*(0.5)^(20-x)
B(13) = (20 C 13)*(0.5)^(13)*(0.5)^(20-13)
B(13) = (77,520)*(0.5)^(13)*(0.5)^(7)
B(13) = 0.073929 approximately
This is the approximate probability exactly thirteen companies send a representative.


These steps are repeated for x = 14, x = 15, all the way up to x = 20


I'll let you do those steps, but you should get these approximate results:
B(14) = 0.036964
B(15) = 0.014786
B(16) = 0.004621
B(17) = 0.001087
B(18) = 0.000181
B(19) = 0.000019
B(20) = 0.000001
All of which are approximate to 6 decimal places.


The last step is to add B(12), B(13), all the way up to B(20)
You should get <font color=red>0.251722</font> when doing so.
There's about a 25.1722% chance of twelve or more companies sending a representative.


Here's one free calculator to check your work
<a href = "https://calculator-online.net/binomial-distribution-calculator/">https://calculator-online.net/binomial-distribution-calculator/</a>
there are tons of other free options out there as well.
</font>