b. Suppose that you talie sample ot S00 aduts If the population proDonan ot 2dul

Question

b. Suppose that you talie sample ot S00 aduts If the population proDonan ot 2dults who watch news videos 1, what is the probabilty that fewer tan hlt in ?our sample wil watch news tdcoz? probablity thust fwer than ha Iha probabitythat twer than hait ot ha adult n thesampclwatch nows vidos Hound bo tour dacimal placa Rs nandad) Discuss the effect f semple ce on thu samping distr but on of de proportion in general aenmeral and the nd t effect on the probabilities p rts(e) A. Inc cas ng the sa le Qize by a actor ot 5 decreascs thc standard mor by actor Th s case, he samping d st but on o t c prcporti n to become more co centated round the ne papuation proport on o 0.51 and decreases the pro bl n part b O B. Tha probabilitiss in parts (a) and ib) ara tha sams Increasing the sampla sb doss not changa tha sampling distribut on ot tha pnapartion OInrca stze by afactor o 5 ncrt tandard err byfacterT caus the samçling datbuton of the proportien to bccome bed around tc true populatien propoticn of 1and incrace the probabilty In part(b). atien proportian fu norases the

Explanation / Answer

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
proportion ( p ) = 0.51
standard Deviation ( sd )= sqrt(PQ/n) = sqrt(0.51*0.49/100)
=0.05
a.
P(X < 0.5) = (0.5-0.51)/0.05
= -0.01/0.05= -0.2
= P ( Z <-0.2) From Standard Normal Table
= 0.4207
b.
P(X < 0.5) = (0.5-0.51)/0.0224
= -0.01/0.0224= -0.4464
= P ( Z <-0.4464) From Standard Normal Table
= 0.3276
c.
option A is

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