find the indicated probabilities using the geometric distribution, the poisson distribution, or the binomial distribution. then determine if the events are unusual. use technology to find the probabilities.

sixty-eight percent of parents of children ages 8-14 say they are willing to get a second or part-time job to pay for their childrens college education. you randomly select six parents. find the probability that the number who say they are willing to get a second or part-time job to pay for their childrens college education is (a) exactly two, (b) less than five, and (c) at least two.

(a) $p(2) = 0.073$
(round to three decimal places as needed.)

(b) $p(x

Question

find the indicated probabilities using the geometric distribution, the poisson distribution, or the binomial distribution. then determine if the events are unusual. use technology to find the probabilities.

sixty-eight percent of parents of children ages 8-14 say they are willing to get a second or part-time job to pay for their childrens college education. you randomly select six parents. find the probability that the number who say they are willing to get a second or part-time job to pay for their childrens college education is (a) exactly two, (b) less than five, and (c) at least two.

(a) $p(2) = 0.073$
(round to three decimal places as needed.)

(b) $p(x < 5) = $
(round to three decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Binomial Probability Formula", "Cumulative Binomial Probability" ], "new_concepts": [], "current_concepts": [ "Binomial Probability Formula", "Cumulative Binomial Probability" ] } ## Identify binomial parameters $$ n = 6, \quad p = 0.68, \quad q = 1 - p = 0.32 $$ ## Calculate the cumulative probability for less than five $$ \begin{aligned} P(X < 5) &= P(X \le 4) = 1 - P(X = 5) - P(X = 6) \ P(X = 5) &= \binom{6}{5} (0.68)^5 (0.32)^1 = 6 \times 0.145393 \times 0.32 \approx 0.27915 \ P(X = 6) &= \binom{6}{6} (0.68)^6 (0.32)^0 = 1 \times 0.098867 \times 1 \approx 0.09887 \ P(X < 5) &\approx 1 - 0.27915 - 0.09887 = 0.62198 \approx 0.622 \end{aligned} $$ ## Verify the result $$ P(X < 5) \approx 0.622 $$ (b) P(X < 5) = 0.622 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Cumulative Binomial Probability" ] }

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QUESTION IMAGE

Question

Explanation:

Identify binomial parameters

Calculate the cumulative probability for less than five

Verify the result

Answer: