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.

a newspaper finds that the mean number of typographical errors per page is four. find the probability that (a) exactly six typographical errors are found on a page, (b) at most six typographical errors are found on a page, and (c) more than six typographical errors are found on a page.

(a) p(exactly six typographical errors are found on a page) =
(round to four 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.

a newspaper finds that the mean number of typographical errors per page is four. find the probability that (a) exactly six typographical errors are found on a page, (b) at most six typographical errors are found on a page, and (c) more than six typographical errors are found on a page.

(a) p(exactly six typographical errors are found on a page) =
(round to four 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": [ "Poisson Distribution", "Poisson Probability Formula" ], "new_concepts": [], "current_concepts": [ "Poisson Distribution", "Poisson Probability Formula" ] } ## Identify the distribution parameters $$ \begin{aligned} &\lambda = 4\ &x = 6\ &P(X = x) = \frac{e^{-\lambda} \lambda^x}{x!} \end{aligned} $$ ## Calculate the probability $$ \begin{aligned} P(X = 6) &= \frac{e^{-4} \cdot 4^6}{6!}\ &= \frac{e^{-4} \cdot 4096}{720}\ &\approx 0.0183156 \cdot 5.68889\ &\approx 0.1041956 \end{aligned} $$ ## Round to four decimal places $$ P(X = 6) \approx 0.1042 $$ (a) P(exactly six typographical errors are found on a page) = 0.1042 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Poisson Probability Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the distribution parameters

Calculate the probability

Round to four decimal places

Answer: