Question

An engineering study indicates that 8.5% of the bridges in a large state are structurally deficient. The state's department of transportation randomly samples 100 bridges. What is the probability that exactly 6 bridges in the sample are structurally deficient

Answer 1

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%