Question

For her final​ project, Stacy plans on surveying a random sample of 40 students on whether they plan to go to Florida for Spring Break. From past​ years, she guesses that about 15​% of the class goes. Is it reasonable for her to use a Normal model for the sampling distribution of the sample​ proportion? Why or why​ not?

Select all that apply.

A. No, because the date​ doesn't meet the Quantitative Data Condition.

B. No, because the data​ doesn't meet the Randomization Condition.

C. ​Yes, because the data meets all the necessary conditions.

D. No, because the date​ doesn't meet the Nearly Normal Condition.

E. No, because the data​ doesn't meet the​ Success/Failure Condition.

F. ​No, because the data​ doesn't meet the​ 10% Condition.

Answer 1

No, because the data​ doesn't meet the​ Success/Failure Condition. (E)

[ explanation:-

given data are:-

sample size (n) = 40

p = 15% = 0.15

q = (1-p ) = (1-0.15) = 0.85

the conditions needed are:-

i).10% condition:-

the sample size ,.i.e, 40 is obviously less than 10% of the number of students in that college.so, this condition is SATISFIED.

ii).independence :-

it is a simple random sample, so, the independence condition is also satisfied.

iii).np 10 and nq10 condition:-

np = (40*0.15) = 6 <10

nq= (40*0.85) = 34 >10

here, np, i.e, the number of success is 6, which is less than 10..which should be greater than or equals 10..hence this condition is VIOLATED]

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