In a taste test of preference among Starbucks, McDonald’s and Dunkin’ Donuts cof
ID: 2922014 • Letter: I
Question
In a taste test of preference among Starbucks, McDonald’s and Dunkin’ Donuts coffee, 50 randomly selected coffee drinkers will each be given samples of the three coffees (in a random order) and asked to state their preference (which of the three they thought tasted the best). Suppose that each of the 50 taste testers really have no preference and will just select a 'favorite' at random.
A.) What is the probability that a taste tester will select Starbucks as the 'favorite'? Bold one.
0.3333 0.6667 0.5 Cannot tell
B.) How many of the taste testers are expected to select Starbucks as the 'favorite'? Bold one.
17 testers 16.67 testers 16 testers Cannot tell
C.) What is the probability that 20 or more of the 50 taste testers will select Starbucks as the 'favorite'? Show all work.
Explanation / Answer
A) Since the taste tester selects a favorite choice at random, probability p = 1/3 = 0.3333.
B) Number of testers n = 50
The number of taste tester expected to select Starbucks as favorite np = 50 * 0.3333 = 16.67 testers
C) Mean = 16.67 Standard deviation = (np(1-p)) = (16.67*0.6667)
= 3.3337
P(X >= 20) = 1 - (X < 20)
Z = (20 - 16.67) / 3.3337
= 0.9989
The probability for Z from table = 0.8411
=> P(X >= 20) = 1 - 0.8411 = 0.1589.
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