a)we had noted that under the assumption that P(Male baby) = P(Female baby)=0.5, Arbuthnott had claimed that

P(# Male babies born in a year > # Female babies born in a year)=0.5

to a very good approximation. Assuming that n= number of babies born in a year is large, show briefly but clearly why Arbuthnott's claim is correct (Hint: Let Y = # of Male babies in n births in the year and then note that # Female babies in n births that year = n-Y)

b)The scores on the GMAT are known to be normally distributed, with the 25thpercentile being a score of 432 and the 90thpercentile being 628 (i.e. this means that 25% of the scores fall below 432 and 90% of the scores fall below 628). A student gets a score of 585. What percentile is his score (i.e. what percent of the scores fall below his score of 585)?