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A restaurant chain wants to create dishes that will attract new clientele. They are interested in adding some vegetarian and vegan options to their menu. A survey revealed that 24% of males and 39% of females order vegetarian while out.
60 clients were randomly selected: 20 men and 40 women.
Let X be the number of males (out of 20) who order vegetarian sometimes.
Let Y be the number of females (out of 40) who order vegetarian sometimes.
Let Z be the total number in the sample who order vegetarian sometimes (out of 60).
ANSWER:
All of the above are true
Good job! X represents the number of veg-friendly males out of a random sample of 20 → X is binomial with n = 20 and p = 0.24. Y represents the number of veg-friendly females out of a random sample of 40 → Y is also binomial with n = 40 and p = 0.39. Z represents the total number of veg-friendly people out of the total sample of 60. Z is not binomial, since the probability of “success” (being veg-friendly) is not the same for all 60 people (0.24 for the 20 males and 0.39 for the 40 females).