Question

A study was conducted to determine if consumers are more likely to choose a vice product (e.g., a candy bar) when their arm is flexed (as when carrying a shopping basket than when their arm is extended (as when pushing a shopping cart). The study measured choice scores (on a scale of 0 to 100, where higher scores indicate a greater preference for vice options) for consumer shopping under each of the two conditions. The average choice score for consumers with a flexed arm was 59, while the average for consumers with an extended arm was 45. For both conditions, assume that the standard deviation of the choice scores is 6. Also assume that both distributions are approximately normally distributed. Complete parts (a) and (b).

(a) In the flexed arm condition, what is the probability that a consumer has a choice score of 57 or greater?

(b) In the extended arm condition, what is the probability that a consumer has a choice score of 57 or greater?

Answer 1

X: choice score for consumers with a flexed arm condition

X follows normal distribution with mean 59 and standard deviation 6

(a)In the flexed arm condition, probability that a consumer has a choice score of 57 or greater = P(X57)

P(X57) = 1 - P(X<57)

Z-score for 57 = (57-59)/ 6 = -2/6 = -0.33

From standrd nomal tables, P(Z<-0.33) = 0.3707

P(X<57) = 0.3707

P(X57) = 1 - P(X<57)=1-0.3707=0.6293

(a)In the flexed arm condition, probability that a consumer has a choice score of 57 or greater = 0.6293

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Y: choice score for consumers with a extended arm condition

Y follows normal distribution with mean 45 and standard deviation 6

(b)In the extended arm condition, probability that a consumer has a choice score of 57 or greater = P(Y57)

P(Y57) = 1 - P(X<57)

Z-score for 57 = (57-45)/ 6 = 12/6 = 2

From standrd nomal tables, P(Z<2) = 0.9772

P(Y<57) = 0.9772

P(Y57) = 1 - P(Y<57)=1-0.9772=0.0228

In the extended arm condition, probability that a consumer has a choice score of 57 or greater = 0.0228

(a)In the flexed arm condition, probability that a consumer has a choice score of 57 or greater = 0.6293

(b)In the extended arm condition, probability that a consumer has a choice score of 57 or greater = 0.0228