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

fifty-one percent of u.s. adults oppose hydraulic fracturing (fracking) as a means of increasing the production of natural gas and oil in the united states. you randomly select five u.s. adults. find the probability that the number of u.s. adults who oppose fracking as a means of increasing the production of natural gas and oil in the united states is (a) exactly two, (b) less than four, and (c) at least three.

(a) p(2) = 0.306
(round to three decimal places as needed.)

(b) p(less than four) =
(round to three decimal places as needed.)

Question

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

fifty-one percent of u.s. adults oppose hydraulic fracturing (fracking) as a means of increasing the production of natural gas and oil in the united states. you randomly select five u.s. adults. find the probability that the number of u.s. adults who oppose fracking as a means of increasing the production of natural gas and oil in the united states is (a) exactly two, (b) less than four, and (c) at least three.

(a) p(2) = 0.306
(round to three decimal places as needed.)

(b) p(less than four) =
(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 $$ n = 5,\quad p = 0.51,\quad q = 1 - p = 0.49 $$ ## Calculate individual probabilities $$ \begin{aligned} P(0) &= \binom{5}{0} (0.51)^0 (0.49)^5 \approx 0.0282 \ P(1) &= \binom{5}{1} (0.51)^1 (0.49)^4 \approx 0.1470 \ P(2) &= \binom{5}{2} (0.51)^2 (0.49)^3 \approx 0.3060 \ P(3) &= \binom{5}{3} (0.51)^3 (0.49)^2 \approx 0.3185 \end{aligned} $$ ## Compute cumulative probability for less than four $$ \begin{aligned} P(\text{less than four}) &= P(X < 4) = P(0) + P(1) + P(2) + P(3) \ &= 0.0282 + 0.1470 + 0.3060 + 0.3185 \ &= 0.7997 \approx 0.800 \end{aligned} $$ (b) P(less than four) = 0.800 { "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 individual probabilities

Compute cumulative probability for less than four

Answer: