How come in a they use a binomial distribution and in b use a normal?

2. Lady Gaga Songs Lee's sister, Emily, is a big fan of Lady Gaga, and 20% of the songs on her iPod are Lady Gaga songs. For the following questions, Emily's iPod is on shuffle and repeat mode, which can be assumed to mean that each song to be played always has the same 20% chance to be a Lady Gaga song (independently of any previously played song). a. If Emily goes for a run and listens to five songs, what is the probability that at least one of them will be from Lady Gaga? We have X=# Lady Gaga songs in the 'sample' of 5 songs, which will be binomial with n = 5 and p = 0.20. P(X 2 1) = 1- P(X = 0) = 1 - [(5 choose 0)(0.20) (0.80)'] = 1 - (0.32768) = 0.67232 _c _~moo' o--.. O---o_o. o b. If Emily listens to her iPod for an entire cross-country flight (exactly 75 songs during the 5 hour flight), what is the approximate probability that at least 14 of the 75 songs she hears are from Lady Gaga? We now have X=# Lady Gaga songs in the 'sample' of 75 songs, which will be approximately Normal with a mean of np = 75(0.20) = 15 songs, and a standard deviation of sqrt[75(0.20)(0.80)] = sqrt(12) = 3.4641 So to nd the probability of at least 14. we rst find Z= it; = 0.29 then using Table A.1 we have the probability of at least 14 to be the area to the right of z = -0.29 which is 1 0.3859 = 0.6141. Final Answer: 0.6723