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enyata [817]
3 years ago
7

An engineering study indicates that 8.5% of the bridges in a large state are structurally deficient. The state's department of t

ransportation randomly samples 100 bridges. What is the probability that exactly 6 bridges in the sample are structurally deficient
Mathematics
1 answer:
Wewaii [24]3 years ago
8 0

Answer:

P(X=6)=(100C6)(0.085)^6 (1-0.085)^{100-6}=0.1063

Then the probability that exactly 6 bridges in the sample are structurally deficient is 0.1063 or 10.63%

Step-by-step explanation:

Let X the random variable of interest "number of bridges in the sample are structurally deficient", on this case we now that:

X \sim Binom(n=100, p=0.085)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

And we want to find this probability:

P(X=6)

And if we use the probability mass function and we replace we got:

P(X=6)=(100C6)(0.085)^6 (1-0.085)^{100-6}=0.1063

Then the probability that exactly 6 bridges in the sample are structurally deficient is 0.1063 or 10.63%

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