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A marketing survey is conducted in which students are to taste two different brands of soft drink. Their task is to correctly identify the brand tasted. A random sample of 180 students is taken. Assume that the students have no ability to distinguish between the two brands. Complete (a) through (d) below. a. What is the probability that the sample will have between 50% and 60% of the identifications correct? (Round to four decimal places as needed.)

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solution:-.

given that n = 180 (number of students)
p = 0.5 (probability of correct identification)

standard deviation = sqrt[p(1-p)/200] = sqrt[(0.5)(0.5)/180]
= 0.0373

(a)p(0.5 < x < 0.6) = p[(0.5 - 0.5) / 0.0373 < Z < (0.6 - 0.5) / 0.0373]
= p(0 < z < 2.6810)
= p(z < 2.6810) - p(z < 0)
= 0.9963 - 0.5
= 0.4963

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