Suppose a simple random sample of size n 1000 is obtained from a population whos

Question

Suppose a simple random sample of size n 1000 is obtained from a population whose size is N-1,500,000 and whose population proportion with a specified characteristic is p= 0.75. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. O A. Approximately normal, #0.75 and :" 0.0002 OB. Approximately nor 0.75 and 0.75 and 00004 00137 OC. Approximately normal, (b) What is the probability of obtaining x 790 or more individuals with the characteristie? P(x2790)-(Round to four decimal places as needed.) (c) What is the probability of obtaining x 720 or fewer individuals with the characteristic? P(XS720)-(Round to four decimal places as needed )

Explanation / Answer

Ans:

a)

mean=0.75

standard deviation=sqrt(0.75*(1-0.75)/1000)=0.0137

Option C is correct.

b)sample proportion=790/1000=0.79

z=(0.79-0.75)/0.0137=2.92

P(z>=2.92)=0.0017

(consider 0.0018 too,as there may be rounding off error)

c)sample proportion=720/1000=0.72

z=(0.72-0.75)/0.013=-2.19

P(z<=-2.19)=0.0142

(consider 0.0143 too,as there may be rounding off error)

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