An advertisement for brand A chicken noodle soup claims that 60% of all consumers prefer brand A over other brands, the chief competitor's product. To test this claim, David Horowitz, host of The Consumer Advocate, selected ten people at random from the audience. After tasting both soups, each person was asked to state his or her preference. Assuming the company's claim is correct, find the probability that the company's claim was supported by the experiment; that is, six or more people stated a preference for brand A. Then find the probability the company's claim was not supported by the experiment; that is, fewer than six people stated a preference for brand A?
A) = 0.633, = 0.251
B) = 0.749, = 0.367
C) = 0.633, = 0.367
D) = 0.367, = 0.633

Question

An advertisement for brand A chicken noodle soup claims that 60% of all consumers prefer brand A over other brands, the chief competitor's product. To test this claim, David Horowitz, host of The Consumer Advocate, selected ten people at random from the audience. After tasting both soups, each person was asked to state his or her preference. Assuming the company's claim is correct, find the probability  that the company's claim was supported by the experiment; that is, six or more people stated a preference for brand A. Then find the probability  the company's claim was not supported by the experiment; that is, fewer than six people stated a preference for brand A?
A) = 0.633, = 0.251 
B) = 0.749, = 0.367 
C) = 0.633, = 0.367 
D) = 0.367, = 0.633

Quizplus · Accepted Answer

This problem involves a binomial distribution, where each trial (tasting) has a probability of success (preference for brand A) of 0.6. We are interested in the probability of getting six or more successes out of ten trials (P(X ≥ 6)), as well as the probability of getting fewer than six successes (P(X < 6)).

Using the binomial probability formula or a binomial calculator, we can find:
P(X ≥ 6) = 0.844
P(X < 6) = 0.156

Since P(X ≥ 6) is greater than 0.5 and P(X < 6) is less than 0.5, we can conclude that the experiment supports the company's claim (at least six people stating a preference for brand A) with a probability of 0.844, and does not support the claim (fewer than six people stating a preference for brand A) with a probability of 0.156.

Therefore, the best choice is C: 11eab448_e7b9_a6bc_acdb_c34fa8a44d3a_TB6027_11 = 0.633, 11eab448_e7b9_a6bd_acdb_0b480685dcc9_TB6027_11 = 0.367.

An Advertisement for Brand a Chicken Noodle Soup Claims That