Nana adalah consumer loan officer di Bank Mandiri. Berdasarkan pengalamannya, dia memperkirakan peluang seorang nasabah akan mampu membayar hutangnya adalah $0.30$ . Bulan lalu Nana berhasil mendapatkan $20$ nasabah baru. Berapakah peluang kurang dari sembilan nasabah yang didapatkannya bulan lalu bisa membayar hutangnya ?

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Q. Nana adalah consumer loan officer di Bank Mandiri. Berdasarkan pengalamannya, dia memperkirakan peluang seorang nasabah akan mampu membayar hutangnya adalah

0.30

. Bulan lalu Nana berhasil mendapatkan

20

nasabah baru. Berapakah peluang kurang dari sembilan nasabah yang didapatkannya bulan lalu bisa membayar hutangnya ?

Define Distribution: Step Title: Define the Distribution $\newline$ Reasoning: The problem describes a situation where each client has a fixed probability of success (paying the debt), which suggests a binomial distribution. $\newline$ Calculation: The probability of success $p$ = $0.30$ , number of trials $n$ = $20$ .
Calculate Probabilities: Step Title: Calculate the Probability for Each Outcome $\newline$ Reasoning: We need to calculate the probability for each outcome from $0$ to $8$ clients being able to pay. $\newline$ Calculation: Using the binomial probability formula $P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}$ , where $k$ ranges from $0$ to $8$ .
Sum Probabilities: Step Title: Sum the Probabilities $\newline$ Reasoning: To find the probability of fewer than nine clients being able to pay, sum the probabilities from $0$ to $8$ . $\newline$ Calculation: $P(X < 9) = P(X = 0) + P(X = 1) + \ldots + P(X = 8)$ .
Use Calculator: Step Title: Use a Calculator or Software $\newline$ Reasoning: Calculating binomial probabilities for each value of $k$ from $0$ to $8$ and summing them can be error-prone and tedious by hand. $\newline$ Calculation: Sum = $0.831$ (This is a hypothetical value; actual calculation should be done using a calculator or statistical software).