not all visitors to a certain companys website are customers. in fact, the website administrator estimates…
not all visitors to a certain companys website are customers. in fact, the website administrator estimates that about $8\\%$ of all visitors to the website are looking for other websites. assuming that this estimate is correct, find the probability that, in a random sample of $4$ visitors to the website, exactly $3$ actually are looking for the website.\n\nround your response to at least three decimal places. (if necessary, consult a list of formulas.)
Answer
Explanation:
Step1: Identify the binomial parameters
The probability of a visitor looking for other websites is $p = 0.08$. The sample size is $n = 4$. We need the probability of exactly $k = 3$ such visitors.
Step2: Apply the binomial probability formula
The formula is $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$. $$P(X = 3) = \binom{4}{3} (0.08)^3 (1 - 0.08)^{4-3}$$
Step3: Calculate the binomial coefficient
$$\binom{4}{3} = \frac{4!}{3!(4-3)!} = 4$$
Step4: Compute the final probability
$$P(X = 3) = 4 \times (0.08)^3 \times (0.92)^1$$ $$P(X = 3) = 4 \times 0.000512 \times 0.92 = 0.00188416$$
Step5: Round to three decimal places
Rounding $0.00188416$ to at least three decimal places. $$0.002$$
Answer:
0.002