Question

4. Thirty-five percent of all first-year college students in the U.S. applied to colleges besides the one they are attending (p = 0.35). You ask a random sample of 1500 first-year college students in the U.S. whether they applied for admission to any other college. Let prepresent the proportion of the college students in the sample who applied to a college besides the one they are attending. [13 pts) a. Check the three conditions necessary to use the Central Limit Theorem for sample proportions. b. Determine the mean and standard deviation of the sampling distribution of p. c Sketch the sampling distribution of p. Label and scale the axis appropriately. d. What is the probability that your sample proportion will be between 0.33 and 0.372

Answer 1

Given that : - n=300 x = 159 D are Given that - P=0.35 n=1500 Here, Sample size is large, Samples independent. O mean - llp = 0.35m 1 Standord deviakus = op - PC1-P). 6. 358O. 1500 INCoil Approximety Normal 0,35

@ P(0.33 < P < 0.37) =P [ 0:33-0035 < P-Po < 037-0:35 | = P1 =1:63 <<< 1:63] 0.0123 Go T 0.0123 J = Plz<1.63) - P[2<-1-63) win <table, 0.9484 -0.0516 -1.63 1.63