Ourrert learning objective: Binomial Distribution Questions Some: Qof 4 points The dones family was one of the first to come to the US. They had 6 chilidren. Assurting that the probsblity of a child heing a gin is Quy, find the protitlity that the dotes farnily that a. at least 5 ginls? The probability that the sones family had at least 5 ginls is Exteryour answer (Repont answer acourate to four cecimal ylaces.) b. at most 3 ginls? ORequinements Emer an imeper or cecimal number The probability that the sones familiy had at most 3 girls is Enteryour answer \( \square \) - (ineport answer accurate to four decimal places.)

Imagine the days of early American settlers when families were larger, and each child was seen as a blessing. The binomial distribution can help us understand events like the Sones family's, where there's a chance of having boys or girls. With a fixed number of children – in this case, 6 – and a consistent probability of having a girl, we can calculate those probabilities using the binomial formula \( P(X=k) = \binom{n}{k} p^k (1-p)^{n-k} \). This mathematical insight gives us the tools to analyze family dynamics from long ago! Now, let’s dive into practical applications! The binomial distribution isn’t just for families; it’s widely used in various fields like medicine, finance, and quality control, helping experts make predictions and assess risk. For instance, say a factory checks products for defects; they can use binomial probabilities to evaluate how many defective items might come from a batch. So every time you see families expand or products get manufactured, remember the power of probability resting behind those moments!