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mash [69]
3 years ago
11

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following p

robability, given the number of trials and
the probability of obtaining a success. Round your answer to four decimal places
PCX > 4), n-8.p -0.7
Mathematics
1 answer:
faltersainse [42]3 years ago
4 0

Answer:

P(X > 4) = 0.8059

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this question, we have that:

n = 8, p = 0.7

We want:

P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 5) = C_{8,5}.(0.7)^{5}.(0.3)^{3} = 0.2541

P(X = 6) = C_{8,6}.(0.7)^{6}.(0.3)^{2} = 0.2965

P(X = 7) = C_{8,7}.(0.7)^{7}.(0.3)^{1} = 0.1977

P(X = 8) = C_{8,8}.(0.7)^{8}.(0.3)^{0} = 0.0576

Then

P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2541 + 0.2965 + 0.1977 + 0.0576 = 0.8059

So

P(X > 4) = 0.8059

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