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 or more:

A researcher wishes to find the probability that more than 80% of a sample of undergraduate students from UNC will be female. He samples the first 20 students that walk into the gym on Monday morning. The population proportion of undergraduate females at UNC is known to be 80.1%.

A researcher wishes to find the probability that more than 16% of a sample of undergraduate students from UNC Charlotte will be between the ages of 25 and 34. She samples the first 75 students that walk into the gym on Monday morning. The population proportion of undergraduates between the ages of 25 and 34 is known to be 14%.

A grad student at UNC wants to know how likely it is that a group of students would be made up of less than 35% graduate students. She will ask 25 of her UNC friends if they are a graduate student or an undergraduate student. The population proportion of grad students and UNC is 37%.

A full-time student at Appalachian State University wants to know how likely it is that a group of students would be made up of more than 85% full-time students. She will randomly ask 85 students their enrollment status. The population proportion of full-time students at Appalachian State is 88%.

Answer 1

When n * p and n * (1-p) are greater than or equal to 10, you can use the normal approximation to sampling distribution of sample proportion to solve a problem.

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

1)A researcher wishes to find the probability that more than 16% of a sample of undergraduate students from UNC Charlotte will be between the ages of 25 and 34. She samples the first 75 students that walk into the gym on Monday morning. The population proportion of undergraduates between the ages of 25 and 34 is known to be 14%.

2)A full-time student at Appalachian State University wants to know how likely it is that a group of students would be made up of more than 85% full-time students. She will randomly ask 85 students their enrollment status. The population proportion of full-time students at Appalachian State is 88%.