Question 1146912: In a recent study 35 percent of people surveyed indicated chocolate was their favorite flavor of ice cream. Suppose we select a sample of 10 people and ask them to name their favorite ice cream flavor.
A: What is the probability that 4 or more name chocolate?
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website! .
It is a binomial distribution type problem where the probability under the question is the sum
P =  (1)
The number of trials is 10;
The indexes of success trials k = 4, 5, 6, 7, 8, 9, 10.
The probability of success trial p = 0.35;
q = 1 - p = 0.65;
C(n,k) = n! / (k! * (n-k)!) are binomial coefficients.
The formula (1) is just a (ready to use) formal mathematical solution, and you may complete calculations manually.
But in nova days the trend is to use TECHNOLOGY for such calculations.
To use the Technology, notice that the sum (1) is equal to 1 -  . (2)
Instead of calculating every term of (1) or (2) manually and then summing them up, you may use Excel function
BINOM.DIST(3, 10, 0.35, TRUE) to calculate the value of in one click
= 0.513827.
Therefore, the value of (2) is equal to 1 - 0.513827 = 0.486173 (approximately). ANSWER
On Excel function BINOM.DIST, see its description everywhere, for example
https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c
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