Question

Which of the following scenarios would it be appropriate to use a normal approximation for the sampling distribution of the sample proportion?

Select one:

A researcher wishes to find the probability that more than 60% of a sample of undergraduate students from UNC will be female. She samples the first 42 students that walk into the gym on Monday morning. The population proportion of undergraduate females at UNC is known to be 60.1%.

A researcher wishes to find the probability that less than 5% of a sample of undergraduate students from Appalachian State University will be between the ages of 25 and 34. He randomly samples 50 undergraduate students from the student database. The proportion of undergraduates between the ages of 25 and 34 is 5.3%.

A grad student at NC state wants to know how likely it is that a group of students would be made up of more than 27% graduate students. She will randomly select 38 students and ask them if they are a graduate student or an undergraduate student. The population proportion of grad students at NC state is 26.6%.

A full-time student at Fayetteville State University wants to know how likely it is that a group of students would be made up of less than 70% full-time students. She will ask 30 people that she sees parking in the parking deck if they are full-time or part-time. The population of full-time students at Fayetteville State is known to be 72%.

Answer 1

Answer:

a)

Given,

Arbitrary examining technique isn't utilized for the number of inhabitants in all undergrad female understudies at UNC.

The initial 42 understudies who stroll into the exercise center on Monday morning isn't chosen aimlessly. Hence, the ordinary guess isn't suitable for this situation.

b)

Given data,

n = 50

p = 5.3% = 0.053

Here p denote the population proportion of under graduate between the ages of 25 and 34 which is 5.3% and the sample selected from the student data base is (n) 50.

np = 50*0.053

= 2.65 < 10

nq = 50*(1 - .053)

= 47.35 > 10

The estimation of np is acquired by duplicating the sample size with populace extent.

The estimation of n(1−p) is gotten by duplicating test size with the distinction in populace extent and one. Check if the two qualities are more prominent than 10.

c)

Give p a chance to signify the populace extent of alumni understudies at NC State which is 26.6%, and the example size (n) is 38.

n = 38

p = 0.266

np = 38 x 0.266

np = 10.108 > 10

nq = 38*(1-0.266)

= 38*0.734

nq = 27.892 > 10

d)

Irregular examining technique isn't utilized for the number of inhabitants in full time understudies at Fayetteville State.

30 individuals that the analyst sees stopping in the stopping deck full time or low maintenance isn't chosen aimlessly. Consequently, the ordinary estimate isn't proper for this situation.