SOLUTION: At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 0.55. Find the probability that in a sample of 14 customers, at least 3 wil

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Question 1209958: At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 0.55. Find the probability that in a sample of 14 customers, at least 3 will order a nonalcoholic beverage.
Note: Round your answer to 4 decimal places.
Find the probability that in a sample of 14 customers, fewer than 4 will order a nonalcoholic beverage.
Note: Round your answer to 4 decimal places.
Found 2 solutions by jramieagle, Edwin McCravy:
Answer by jramieagle(1)   (Show Source): You can put this solution on YOUR website!
This is a case of Binomial Probability distribution.
Here n=14, x>=3 and p=0.55. 1-p = 1-0.55 = 0.45
Now use the formula to calculate probability:
P(X>=3) = P(3)+P(4)+ -----+P(14)
This calculation becomes very lengthy, hence you may want to use a table or t technology( a calculator or software) I used an online probability calculator
P(X>=3) = refer to the picture attached.

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Do you have a TI-84 Plus?

Let's do the second one first, as it's more straightforward. 

2nd 
vars
Scroll down to B:binomcdf
enter

        binomcdf
trials:14
p:0.55
x value:3
Paste

[The reason for 3 in x-value is because the calculator understands 3 as
 "3 or less", which is the same as "fewer than 4".

Scroll to Paste
enter
you see binomcdf(14,0.55,3)
enter

0.011430528

-----------------

The first one:

You will have to first calculate the probability of the complement event,
then subtract from 1.

The complement of " at least 3 " is " 2 or fewer "

2nd 
vars
Scroll down to B:binomcdf
enter

        binomcdf
trials:14
p:0.55
x value:2
Paste

[The reason for 2 in x-value is because the calculator understands 2 as
 "2 or less"

Scroll to Paste
enter
you see binomcdf(14,0.55,3)
enter

0.002150974  

But that's not the answer. You must subtract from 1.

1 - 0.002150974

0.997849026

Round to 4 decimal places.

Edwin
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