Suppose a simple random sample of size n=200 is obtained from a population who\'

Question

Suppose a simple random sample of size n=200 is obtained from a population who's size is N=25,000 q d whose population proportion with a specified characteristic is p=0.65. A) Is the sampling distribution of P approximately normal? Why? B) What is the probability of obtaining X=136 or more individuals from the 200 with the characteristic? That is, what is P? (P > or equal to 0.68)? C) What is the probability of obtaining x=118 or fewer individuals from the 200 with the characteristic?
Suppose a simple random sample of size n=200 is obtained from a population who's size is N=25,000 q d whose population proportion with a specified characteristic is p=0.65. A) Is the sampling distribution of P approximately normal? Why? B) What is the probability of obtaining X=136 or more individuals from the 200 with the characteristic? That is, what is P? (P > or equal to 0.68)? C) What is the probability of obtaining x=118 or fewer individuals from the 200 with the characteristic?
A) Is the sampling distribution of P approximately normal? Why? B) What is the probability of obtaining X=136 or more individuals from the 200 with the characteristic? That is, what is P? (P > or equal to 0.68)? C) What is the probability of obtaining x=118 or fewer individuals from the 200 with the characteristic?

Explanation / Answer

a) Yes because np > 5

b)

miu = 0.65*200 = 130

SD = srqt ( 0.65*0.35 *200) = 6.75

P( z > 136 - 130 / 6.75 )

P( z > 0.89 ) = 0.1867

c)

P( z < 118 - 130 / 6.75 )

P( z < -1.78 ) = 0.0375

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