An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Calculate the probability that a randomly selected individual is 35 to 44 years of age, given the individual is less likely to buy a product emphasized as "Made in America": 65 6 ≈ 0.092 .
Calculate the probability that a randomly selected individual is less likely to buy a product emphasized as "Made in America," given the individual is 35 to 44 years of age: 536 6 ≈ 0.011 .
Calculate the probability that a randomly selected 18- to 34-year-old is more likely to buy a product emphasized as "Made in America": 537 234 ≈ 0.436 .
Calculate the probability that a randomly selected individual is more likely to buy a product emphasized as "Made in America": 2152 1325 ≈ 0.616 . Since 0.436 < 0.616 , 18- to 34-year-olds are less likely to buy a product emphasized as "Made in America" than individuals in general.
Explanation
Analyze the problem and data We are given a contingency table that summarizes the results of a Harris Poll. We need to calculate conditional probabilities based on the data in the table and compare two probabilities to answer the question.
Calculate P(35-44 | Less likely) (a) We want to find the probability that a randomly selected individual is 35 to 44 years of age, given the individual is less likely to buy a product emphasized as "Made in America". This is a conditional probability. Let A be the event that an individual is 35-44 years old, and B be the event that an individual is less likely to buy the product. We want to find P ( A ∣ B ) = P ( B ) P ( A ∩ B ) .
From the table, the number of individuals who are 35-44 years old and less likely to buy the product is 6. The total number of individuals who are less likely to buy the product is 65. The total number of individuals surveyed is 2152. Therefore, P ( A ∣ B ) = 65/2152 6/2152 = 65 6 ≈ 0.092
Calculate P(Less likely | 35-44) (b) We want to find the probability that a randomly selected individual is less likely to buy a product emphasized as "Made in America", given the individual is 35 to 44 years of age. This is a conditional probability. We want to find P ( B ∣ A ) = P ( A ) P ( A ∩ B ) .
From the table, the number of individuals who are 35-44 years old and less likely to buy the product is 6. The total number of individuals who are 35-44 years old is 536. Therefore, P ( B ∣ A ) = 536/2152 6/2152 = 536 6 = 268 3 ≈ 0.011
Compare probabilities and conclude (c) We want to determine if 18- to 34-year-olds are more likely to buy a product emphasized as "Made in America" than individuals in general. Let C be the event that an individual is 18-34 years old, and D be the event that an individual is more likely to buy the product. We need to compare P ( D ∣ C ) with P ( D ) .
P ( D ∣ C ) = P ( C ) P ( D ∩ C ) = 537/2152 234/2152 = 537 234 ≈ 0.436 P ( D ) = 2152 1325 ≈ 0.616 Since 0.436 < 0.616 , 18- to 34-year-olds are less likely to buy a product emphasized as "Made in America" than individuals in general.
Examples
Understanding consumer preferences based on demographics is crucial for businesses. For example, a company might use this type of analysis to tailor its marketing campaigns to different age groups. If younger adults are less swayed by 'Made in America' labels, the company might focus on other product attributes when advertising to this group, such as sustainability or technological innovation.
