. A recent report stated that 15% (0.15) of all men in the U.S. are left-handed.
ID: 3359683 • Letter: #
Question
. A recent report stated that 15% (0.15) of all men in the U.S. are left-handed. A random sample of 250 men is selected to further study this question, A. What is the Shape, Mean (expected value) and standard deviation of the sampling distribution of the sample proportion for samples of size 250? B. What is the probability that the sample proportion for a sample of size 250 is greater than 10% (0.10)? C. What is the probability that the sample proportion for a sample of size 250 is between 12% (0.12) and 18% (0.18)? show work
Explanation / Answer
as np and n(1-p) both are greater then 10
hence shape of sampling distribution is approximately normal and mean of sampling distribution of the sample proportion =p=0.15
and standard deviation of the sampling distribution =(p(1-p)/n)1/2 =0.0226
B) probability that the sample proportion for a sample of size 250 is greater than 10% =P(X>0.10)
=1-P(X<0.10)=1-P(Z<(0.10-0.15)/0.0226)=1-P(Z<-2.2140)=1-0.0134 =0.9866
C) probability that the sample proportion for a sample of size 250 is between 12% and 18% =P(0.12<X<0.18)
=P((0.12-0.15)/0.0226<Z<(0.18-0.15)/0.0226)=P(-1.3284<Z<1.3284)=0.9080-0.0920=0.8160
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.