Question

Suppose a simple random sample of size n=200 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p=0.2. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Approximately normal because ns0.05N and np(1 :p) < 10. OB. Not normal because n s 0.05N and np(1-P) < 10. OC. Not normal because ns0.05N and np(1-P) 10. OD. Approximately normal because n s 0.05N and np(1 - p)2 10 Determine the mean of the sampling distribution of p. HA= (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. CA= (Round to six decimal places as needed) (b) What is the probability of obtaining x = 46 or more individuals with the characteristic? That is what is PP20.23)? PC 20.23)= (Round to four decimal places as needed) (c) What is the probability of obtaining x = 38 or fewer individuals with the characteristic? That is what is PP SO. 19? PÔS0.19) - (Round to four decimal places as needed.)

Answer 1

D. Aproximately normal because n <0.05N and np (1-p)>10. My = p=0.2 p(1-p) 0.2(1-02) 200 = 0.028284

P(9 20.23)=1-P(P<0.23) =1-P Ô-P<0.23-0.2 0.028284 =1-P(z 51.06) =1-0.8554 = 0.1446 PLØS0.19) = P S S 0.025284) =1-P(25-0.35) =1-0.3632 = 0.6368