fmas6855

27.03.2020 • 

Mathematics

A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Do the data appear to confirm the belief that one design is just as likely to be selected as another? Explaindesign number of times preferred1 52 153 304 405 10

Ответ:

alex24gonzales

16.11.2022

Mathematics

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Step-by-step explanation:

Given ;

Sample size, n = 15probability of a first pitch strike, p = 0.56Probability of not first pitch strike ; q = 1 - p = 1 - 0.56 = 0.44Applying binomial distribution ; P(X = r) = nCr x P^r x (q)^n-r

a) P ( X = 13 ) = C(15,13) x 0.56^13 x (1-0.56)^2 = 0.0108

b) Mean = np = 15 x 0.56= 8.400

Standard deviation = √(np(1-p)) = √(15 x 0.56 x (1-0.56)) = 1.9225

c) P(X>10) = 1 - P(X≤10) = 1 - 0.8633 = 0.1367

d) P(X≥12) = P(X=12) + P(X=13) + P(X=14) + P(X=15) = 0.0498

e) P(Y=3) = C(3,1) x 0.56^1 x (1-0.56)^2 x 0.56 = 0.1821

f) P(Y=2) = C(2,1) 0.56^1 x (1-0.56)^1 x 0.56 = 0.2760

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