SOLUTION: 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 proba

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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) About Me  (Show Source):
You can put this solution on YOUR website!

+P%28X%3C5%29, +n=7, +p=0.3
What is binomial distribution?
In binomial distribution for number trials we are investigating the probability of getting a success remain the same.

+n+= number of trails,
+p = probability of success
+x = the number of success
given that +P%28x%3C5%29, so use +x=0,1,2,3,4

+p%28x%3C5%29=p%28x=0%29%2Bp%28x=1%29%2B+p%28x=2%29%2Bp%28x=3%29%2Bp%28x=4%29

+p%28x%3C5%29=0.0823543%2B0.2470629%2B0.3176523%2B0.2268945%2B0.0972405
+p%28x%3C5%29=0.9712045
+p%28x%3C5%29=0.9712

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

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