according to a recent survey, 85% of high school sutdents own a personal media player. what is the probability that 6 out of 10 random high school students own a personal media player?

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%.

binomial distribution, theprobabilitythat 6 out of 10randomhigh school students own a personal media player is4%.Binomial distribution:successfultrailsProbabilityof failureSuccessrate = 6percentage= 85%binomialdistribution, Substituting in values for this problem, n=10, p=0.85, and X=6 on the formula, then we get,probabilityas 4%.Binomial distributionhere.