Question

1. According to data from last year, 67% of Zed-Mart shoppers tried to take advantage of Blazing Purple Specials. In order to decide how many such specials to offer this year, the corporation decides to take a SRS of 100 of their shoppers and ask if they plan to take advantage of Blazing Purple Specials.

(a) Describe the sampling distribution, assuming results will be similar to last year. Include the expected center, variability, and whether or not the sampling distribution would be approximately normal (and why; no credit without the relevant number(s); loss of credit for irrelevant information). Keep at least 4 meaningful figures on the standard deviation.

Center: ____________                                                 Variability: ____________

Normal? ( Yes | No ) Because: ___________________________________________________________

(b) Find the probability that less than 60% of the sample would plan to take advantage of Blazing Purple Specials.                                                                                                                                                          ____________

(d) Why would we have good reason to believe something was going to be different this year if more than 90% of the sample said they planned to take advantage of Blazing Purple Specials? (Hint: Empirical Rule)

_____________________________________________________________________________________

Answer 1

centre = p = 0.67
sd = sqrt(pq/n) = sqrt(0.67* 0.33 / 100) = 0.047021

Normal - yes n = 100 > 30 by central limit theorem

Z = (p^ -p)/sqrt(pq/n)
b)
P(p^ < 0.60)
= P(Z < ( 0.6 - 0.67) / 0.047021)
= P(Z < -1.4887 )
= 0.0683

d)

Z-score = (0.9 - 0.67)/0.047021
= 4.8914

since Z > 2

we have good reason to believe something was going to be different this year if more than 90% of the sample said they planned to take advantage of Blazing Purple Specials

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