Question

2) In a recent poll, the Gallup Organization found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. Suppose a survey of a random sample of 500 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. Use the normal approximation to the binomial to approximate the probability that a. Exactly 270 of those surveyed feel the state of moral is poor. b. No more than 230 of those survey feel the state of morals is poor. C. More than 255 of those surveyed feel the state of moral is poor. d. Between 225 and 255 adult Americans inclusive, believe the state of morals is poor. e. At least 265 adult Americans believe the state of morals is poor.

Answer 1

112 Z 400 29.09 09. p = 0.45, u= mb= 500x 0.45- 225 * O: Jobci-p) - 1225*0.55 = 1123.75 PX 2= * . *-225 where x: No of people who S feel state of moral is poor. @P(X=270) = P(269.5<x< 270.5) = P(269.5-275<z220.5. 225 ) 1123.75^^ V 123.75 ) 4.00<2<4.09) = 0.0000 P(x230)= P(x<230.5)<di = Plz< 230.5-225)- PIZ<0.49) 1123.75 10.6879 © P(x>255)= P(x2256)- P(x>255.5) = Plz> 255.5-2251 - Plz> 2.74) V123.75! 2=2.14 10.0031 @ P(225€ *3255)- P(22454 x<255.5) = P(-0.04<Z20.2.74)= 0.0160+0.4969210.5129 © P*3265)= P(x>20405) - PIZ> 264.5-225) Vi23.75 = P(z>3.55) - 10.0002 Z-0.49