Question

(#9)

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=0.4. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Not normal because ns0.05N and np(1-P) 10. OB. Not normal because ns0.05N and np(1-P) < 10. OC. Approximately normal because ns 0.05N and np(1-P) < 10. OD. Approximately normal because ns0.05N and np(1-P) 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. 0A (Round to six decimal places as needed.) (b) What is the probability of obtaining x = 90 or more individuals with the characteristic? That is, what is P(p 20.45)? PO 20.45) = (Round to four decimal places as needed.) (c) What is the probability of obtaining x = 74 or fewer individuals with the characteristic? That is, what is PP S 0.37)? PPS 0.37)- (Round to four decimal places as needed.)

Answer 1

Sol: a) The distoibution of the values of sample proportion in repeated samples is called the sampling distribution Of . P is normally distributed with a mean of My =p and a Standard deviation Op = P(1-D as long as the sample - size n is laage enough. The connection is to requise - both np and mp (1-P) to be atleast 10. Hence, ß is approximately normal because mp(1-P) zlo. n and also no.05N. Answer :-option D. Mean of the sampling distibution of is, M=P = 0.4) Standard deviation of the sampling distribution of Øis, - 104 (0.6)24 Jocola V 200 200 0.034641

b) PCộ 20.45) - D 15-P 1 PCI- = P(z 2 coucun) 0.45-0.4 근그 0.034641 0.05 del z plzz 302464) se banque bore op (z z 1,44337) pcê sous) - 0.0745) OP C82033) _ p (= FP < 0.3.80) = Plze odstrany) -> p (22 porn) : -P (250.866025) >>0.1932 [PlP<0.37) = 0.1432 0.1932