8. A recent report stated that 15% (0.15) of all men in the US. are left- handed

Question

8. A recent report stated that 15% (0.15) of all men in the US. 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)? /O

Explanation / Answer

a)here p=0.15 and n=250

therefore np>5 as well n(1-p)>5 therefore

shape is approximately normal

with expected proportion =0.15

and sampling distribution of sample proportion =(p(!-p)/n)1/2 =0.0226

b) probability that the sample proportion is greater then 10% =P(X>0.10)=1-P(X<0.10)=1-P(Z<(0.1-0.15)/0.0226)

=1-P(Z<-2.2140)=1-0.0134 =0.9866

c) probability=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

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