Question 1203846: Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X<5), n=7, p=0.3
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20849)   (Show Source):
Answer by math_tutor2020(3817)  (Show Source):
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I'll show various methods to compute the answer using a TI84/TI83 calculator and spreadsheet.
There are many online calculators that will do the same such as this one here
https://www.gigacalculator.com/calculators/binomial-probability-calculator.php
and this one as well
https://www.omnicalculator.com/statistics/binomial-distribution
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TI83 or TI84
Press the button labeled "2ND"
Press the "VARS" key
Scroll down quite a bit until reaching "binomCDF"
The template is
binomCDF(n,p,x)
n = sample size
p = probability of success
x = number of successes
In this case:
n = 7
p = 0.3
x = 4
So you'll type in:
binomCDF(7,0.3,4)
The result of this calculation is approximately 0.9712
There's about a 97.12% chance of having less than 5 successes.
Review this page for more info and further examples
https://www.statology.org/binomial-probabilities-ti-84-calculator/
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On a spreadsheet, we'll use the command binomDist
The input we'll do is =binomDist(4,7,0.3,1)
The equal sign needs to be put up front to apply the calculation.
Otherwise, the spreadsheet will treat it as plaintext.
The general template is
=binomDist(x,n,p,c)
where x,n,p were mentioned earlier. It's unfortunate the order isn't the exact same as the TI84. So be careful if you tend to use both TI84 and spreadsheets.
The c refers to "cumulative"
c = 0 = not cumulative, i.e. use a binomial PDF
c = 1 = cumulative, i.e. use a binomial CDF
The result of the spreadsheet calculation should agree with the TI84.
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Answer: 0.9712
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