Answer :
As per the binomial distribution, the probability that 6 out of 10 random high school students own a personal media player is 4%.
Binomial distribution:
The general formula to calculate the binomial distribution is written as,
P = aCx pˣ (1 - p)ᵃ⁻ˣ
Where,
x = Total number of successful trails
a = Total number of events
p = Probability of success
1 – p = Probability of failure
nCr = [n!/r!(n−r)]!
Given,
According to a recent survey, 85% of high school students own a personal media player.
Here we need to find the probability that 6 out of 10 random high school students own a personal media player.
While we looking into the given question,
Total number of student = 10
Success rate = 6
Probability percentage = 85%
When we convert this into decimal then we get the probability as 0.85.
Now, according to the binomial distribution, Substituting in values for this problem, n=10, p=0.85, and X=6 on the formula, then we get,
=> P = [10!/6!4!] x (0.85)⁶ x(1- 0.85)¹⁰⁻⁶
When we simplify this one then we get the probability as,
=> P = 0.04
When we convert this into percentage, then we get the probability as 4%.
To know more about Binomial distribution here.
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