Last week, a flower delivery business conducted a survey on customer happiness. They found that 56% of their customers were "pleased" with the service. If the company surveys 4 of their customers the next week, what is the probability that exactly 1 is pleased? Write your answer as a decimal rounded to the nearest thousandth. ____

Use Binomial Probability Formula: Use the binomial probability formula: P(X = k) = C(n, k) * (p)^k * (1-p)^(n-k). Here, n = 4, k = 1, and p = 0.56.Calculate C(4, 1): Calculate C(4, 1) using the formula n! / (k! (n - k)!). So, C(4, 1) = 4! / (1! * (4 - 1)!) = 4 / 1 = 4.Compute (0.56)^1: Compute (0.56)^1 which is just 0.56.Calculate (1 - 0.56)^(4 - 1): Calculate (1 - 0.56)^(4 - 1) which is (0.44)^3. So, (0.44)^3 = 0.44 * 0.44 * 0.44 = 0.085184.Multiply Values Together: Multiply all the values together: P(X = 1) = 4 * 0.56 * 0.085184. So, P(X = 1) = 4 * 0.56 * 0.085184 = 0.1905664.Round to Nearest Thousandth: Round the answer to the nearest thousandth: 0.1905664 rounds to 0.191.

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Last week, a flower delivery business conducted a survey on customer happiness. They found that $56\%$ of their customers were ＂pleased＂ with the service. $\newline$ If the company surveys $4$ of their customers the next week, what is the probability that exactly $1$ is pleased? $\newline$ Write your answer as a decimal rounded to the nearest thousandth. $\newline$ ____ $\newline$

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Math Problems

Algebra 2

Find probabilities using the binomial distribution

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Q. Last week, a flower delivery business conducted a survey on customer happiness. They found that

56\%

of their customers were ＂pleased＂ with the service.

\newline

If the company surveys

4

of their customers the next week, what is the probability that exactly

1

is pleased?

\newline

Write your answer as a decimal rounded to the nearest thousandth.

\newline

____

\newline

Use Binomial Probability Formula: Use the binomial probability formula: $P(X = k) = C(n, k) \cdot (p)^k \cdot (1-p)^{(n-k)}$ . Here, $n = 4$ , $k = 1$ , and $p = 0.56$ .
Calculate $C(4, 1)$ : Calculate $C(4, 1)$ using the formula $\frac{n!}{k!(n - k)!}$ . So, $C(4, 1) = \frac{4!}{1! \times (4 - 1)!} = \frac{4}{1} = 4$ .
Compute $(0.56)^1$ : Compute $(0.56)^1$ which is just $0.56$ .
Calculate $(1 - 0.56)^{(4 - 1)}$ : Calculate $(1 - 0.56)^{(4 - 1)}$ which is $(0.44)^3$ . So, $(0.44)^3 = 0.44 \times 0.44 \times 0.44 = 0.085184$ .
Multiply Values Together: Multiply all the values together: $P(X = 1) = 4 \times 0.56 \times 0.085184$ . So, $P(X = 1) = 4 \times 0.56 \times 0.085184 = 0.1905664$ .
Round to Nearest Thousandth: Round the answer to the nearest thousandth: $0.1905664$ rounds to $0.191$ .