Which of the following scenarios would it be appropriate to use normal approxima

Question

Which of the following scenarios would it be appropriate to use normal approximation for the sampling distribution of the proportion? Select all that apply.

Select one or more:

A researcher wishes to find the probability that less than 40% of a sample of undergraduate students from UNC will be male. He samples the first 20 students that walk into the gym on Monday morning. The population proportion of undergraduate males at UNC is known to be 41.1%

A researcher wishes to find the probability that more than 15.5% of a sample of undergraduate students from Winston Salem State University will be between the ages of 25 and 34. He randomly samples 70 undergraduate students from the student database. The population proportion of undergraduates between the ages of 25 and 34 is 14.9%

A grad student at East Carolina wants to know how likely it is that a group of students would be made up of more than 25% graduate students. She will randomly select 45 students and ask them if they are a graduate student or an undergraduate student. The population proportion of grad students and East Carolina is 22.0%.

A full time student at UNC Central University wants to know how likely it is that a group of students would be made up of less than 75% full time students. She will ask 40 students that she sees parking in the parking deck if they are full time or part time. The population proportion of full time students at UNC Central is 77%.

Explanation / Answer

Solution:

These two apply

A grad student at East Carolina wants to know how likely it is that a group of students would be made up of more than 25% graduate students. She will randomly select 45 students and ask them if they are a graduate student or an undergraduate student. The population proportion of grad students and East Carolina is 22.0%.

A full time student at UNC Central University wants to know how likely it is that a group of students would be made up of less than 75% full time students. She will ask 40 students that she sees parking in the parking deck if they are full time or part time. The population proportion of full time students at UNC Central is 77%.

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