Question

Suppose a simple random sample of size nequals1000 is obtained from a population whose size is Nequals2 comma 000 comma 000 and whose population proportion with a specified characteristic is p equals 0.44 . Complete parts​ (a) through​ (c) below. ​(a) Describe the sampling distribution of ModifyingAbove p with caret.

A. Approximately​ normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0004

B. Approximately​ normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0157

C. Approximately​ normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0002

​(b) What is the probability of obtaining xequals460 or more individuals with the​ characteristic? ​P(xgreater than or equals460​)equals nothing ​(Round to four decimal places as​ needed.)

​(c) What is the probability of obtaining xequals410 or fewer individuals with the​ characteristic? ​P(xless than or equals410​)equals nothing ​(Round to four decimal places as​ needed.)

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.4400
sample size       =n=	1000
std error of proportion=σp=√(p*(1-p)/n)=	0.0157

B. Approximately​ normal μp= 0.44 and σp=0.0157

b)

probability =P(X>0.46)=P(Z>(0.46-0.44)/0.016)=P(Z>1.27)=1-P(Z<1.27)=1-0.898=0.1020

c)

probability =P(X<0.41)=(Z<(0.41-0.44)/0.016)=P(Z<-1.9112)=0.0281