Complete the following problems: In the city of Raccoon City, 65% of the population have been infected by a mutagenic pathogen known as the T-Virus. Suppose 12 residents of Raccoon City were selected at random. (a) What is the probability that half of those selected have been infected by the T-Virus? (b) What is the probability that at least 8 of those selected have been infected by the T-virus?
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Given: - Probability of being infected by the T-Virus, P = 0.65 - Number of residents selected, N = 12 Using the binomial distribution formula: \[ P(X = 6) = \binom{12}{6} \times (0.65)^6 \times (1-0.65)^{12-6} \] \[ P(X = 6) = \binom{12}{6} \times (0.65)^6 Show more…
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In the city of Raccoon City, 65% of the population have been infected by a mutagenic pathogen known as the T-Virus. Suppose 12 residents of Raccoon City were selected at random. (a) What is the probability that half of those selected have been infected by the T-Virus? (b) What is the probability that at least 8 of those selected have been infected by the T-Virus?
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In a large population, 65 % of the people have been vaccinated. If 4 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated? Give your answer as a decimal (to at least 3 places) or fraction.
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Based on data from the Statistical Abstract of the United States, 112 th edition, only about $14 \%$ of senior citizens $(65$ years old or older) get the flu each year. However, about $24 \%$ of the people under 65 years old get the flu each year. In the general population, there are $12.5 \%$ senior citizens $(65$ years old or older). (a) What is the probability that a person selected at random from the general population is a senior citizen who will get the flu this year? (b) What is the probability that a person selected at random from the general population is a person under age 65 who will get the flu this year? (c) Answer parts (a) and (b) for a community that is $95 \%$ senior citizens. (d) Answer parts (a) and (b) for a community that is $50 \%$ senior citizens.
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