Questions: At a music store in New York City, 46 people entering the store were selected at random and were asked to choose their favorite type of music. Of the 46, 10 chose rock, 12 chose country, 2 chose classical and 22 chose something other than rock, country, or classical. a) Determine the empirical probability that the next person entering the store favors rock music. b) Determine the empirical probability that the next person entering the store favors country music. c) Determine the empirical probability that the next person entering the store favors something other than rock, country, or classical music. a) The empirical probability that the next person entering the store favors rock music is (Simplify your answer.) b) The empirical probability that the next person entering the store favors country music is (Simplify your answer.) c) The empirical probability that the next person entering the store favors something other than rock, country or classical music is (Simplify your answer.)

At a music store in New York City, 46 people entering the store were selected at random and were asked to choose their favorite type of music. Of the 46, 10 chose rock, 12 chose country, 2 chose classical and 22 chose something other than rock, country, or classical. a) Determine the empirical probability that the next person entering the store favors rock music. b) Determine the empirical probability that the next person entering the store favors country music. c) Determine the empirical probability that the next person entering the store favors something other than rock, country, or classical music. a) The empirical probability that the next person entering the store favors rock music is (Simplify your answer.) b) The empirical probability that the next person entering the store favors country music is (Simplify your answer.) c) The empirical probability that the next person entering the store favors something other than rock, country or classical music is (Simplify your answer.)
Transcript text: At a music store in New York City, 46 people entering the store were selected at random and were asked to choose their favorite type of music. Of the 46,10 chose rock, 12 chose country, 2 chose classical and 22 chose something other than rock, country, or classical. a) Determine the empirical probability that the next person entering the store favors rock music. b) Determine the empirical probability that the next person entering the store favors country music. c) Determine the empirical probability that the next person entering the store favors something other than rock, country, or classical music. a) The empirical probability that the next person entering the store favors rock music is $\square$ (Simplify your answer.) b) The empirical probability that the next person entering the store favors country music is $\square$ (Simplify your answer.) c) The empirical probability that the next person entering the store favors something other than rock, country or classical music is $\square$ (Simplify your answer.)
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Solution

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Solution Steps

Step 1: Total Number of People Surveyed

The total number of people surveyed, \(N\), is 46.

Step 2: Calculation of Empirical Probabilities

The empirical probability of favoring a particular category is calculated using the formula: $$P(category) = \frac{n_{category}}{N}$$ where \(n_{category}\) is the number of people who chose that category.

For each music category, the empirical probabilities are calculated as follows:

  • Rock: $$P(rock) = \frac{10}{46} = \frac{5}{23}$$
  • Country: $$P(country) = \frac{12}{46} = \frac{6}{23}$$
  • Classical: $$P(classical) = \frac{2}{46} = \frac{1}{23}$$
  • Other: $$P(other) = \frac{22}{46} = \frac{11}{23}$$

Final Answer:

The empirical probabilities of favoring each music category are:

  • Rock: 5/23
  • Country: 6/23
  • Classical: 1/23
  • Other: 11/23
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