Homework: Homework 6 Score: 0.17 of 1 pt HYV Score: 56.94%, 3.42 of 6 pts 7.3.13

Question

Homework: Homework 6 Score: 0.17 of 1 pt HYV Score: 56.94%, 3.42 of 6 pts 7.3.13-T A marketing survey ts conducted in which students are to taste two different brands of soft drink Their task is to correctly identty 190 a. (Round to four decimal places as needed.) The pro atlity is 90% tat te sample perce tage is contar ed within what symmetrical In its of the popula on percentage? identi percentage The lower linit is The upper limit is (Round to four decimal places as needed.) tre imts of the population at ework: Homework 6 Save Score: 0.5 of 1 p 3... e Answered 9:10 am

Explanation / Answer

n = 190 (number of students)

p = 0.5 (probability of correct identification)

standard deviation = sqrt [p(1-p)/n] =    [0.5x0.5/190] =      0.25/190 = 0.001315789 = 0.0362

µ = 0.5 (student have no ability to distinguish between both the samples)

standard deviation = 0.0362

standardize x to z = (x- µ)/standard deviation

P(0.5 < x < 0.6) = P(0.5 - 0.5)/ 0.0362 < Z < (0.6 - 0.5) / 0.0362

= P(0 < Z < 2.7624) =   0.9971 - 0.5 = 0.4971

b. From the normal probability table

P(-1.645 < Z < 1.645) = 0.90

z = (x- µ)/ standard deviation

(z x standard deviation) + µ = x     0.0592

therefore,

(z X sd) + µ) < (z X sd) + µ)

(-1.645 x 0.0362) + 0.5)   < Z = (1.645 x 0.0362) + 0.5)

0.4404 to 0.5595 = 44.04 % to 55.95%

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