Please give answer and work. Thanks. Which of the following scenarios would it b
ID: 3069749 • Letter: P
Question
Please give answer and work. Thanks.
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 25% of a sample of undergraduate students from Winston Salem State University will be male. He randomly samples 42 undergraduate students from the student database. The population proportion of undergraduate males at WSSU is known to be 29.3% A researcher wishes to find the probability that more than 1 1 % of a sample of undergraduate students from East Carolina State University will be between the ages of 25 and 34. He samples the first 105 students that walk into the gym on Monday morning The population proportion of undergraduates between the ages of 25 and 34 is 9.9%. x A grad student at UNC Asheville wants to know how likely it is that a group of students would be made up of more than 5% graduate students. She will ask 40 of her friends if they are a graduate student or an undergraduate student. The population proportion of grad students at UNC Asheville is 1.3%. A full time stude time students. She will randomly ask 60 students their enrollment status. The population proportion of full time students at UNC Wilmington is 85% nt at UNC Wilmington wants to know how likely it is that a group of students would be made up of more than 90% fullExplanation / Answer
Scenerios appropriate to use normal approximation :
(a) & (b)
EXPLANATION:
(a)
n = 42
p = 0.293
np = 42 X 0.293 = 12.306 > 10
q = 1 - p = 0.707
nq = 42 X 0.707 = 29.694 > 10
So,
Conditions are satisfied.
(b)
n = 105
p = 0.099
np = 105 X 0.099 = 10.395 > 10
q = 1 - p = 0.901
nq = 105 X 0.901 = 94.605 > 10
So,
Conditions are met.
(c)
n = 40
p = 0.013
np = 40 X 0.013 = 0.52
This is not greater than 10. So, Contion is not met.
(d)
n = 60
p = 0.85
np = 60 X 0.85 = 51 > 10
q = 1 - p = 0.15
nq = 60 X 0.15 = 9
This is not greater than 10.
So,
Condition is not met.