Question

AN ARTICLE STATED THAT “INTERNAL SURVEYS PAID FOR BY DIRECTORY ASSISTANCE PROVIDERS SHOW THAT EVEN THE MOST ACCURATE COMPANIES GIVE OUT WRONG NUMBERS 15% OF THE TIME.” ASSUME THAT YOU ARE TESTING SUCH A PROVIDER BY MAKING 10 REQUESTS AND ALSO ASSUME THAT THE PROVIDER GIVES THE WRONG TELEPHONE NUMBER 15% OF THE TIME. FIND THE PROBABILITY OF GETTING ONE WRONG NUMBER.

Answer 1

Using the binomial distribution, there is a 0.3474 = 34.74% probability of getting one wrong number.

What is the binomial distribution formula?

The formula is:

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

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

The parameters are:

• x is the number of successes.

• n is the number of trials.

• p is the probability of a success on a single trial.

For this problem, the values of the parameters are given by:

p = 0.15, n = 10.

The probability of getting one wrong number is P(X = 1), hence:

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

P(X = 1) = C(10,1) x (0.15)¹ x (0.85)^9 = 0.3474

0.3474 = 34.74% probability of getting one wrong number.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

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