When testing a method of gender selection, we assume that the rate of female births is 50%, and we reject that assumption if we get results that are unusual in the sense that they are very unlikely to occur with the 50% rate. In a preliminary test of the XSORT method of gender selection, 14 births included 13 girls.
a. Assuming a 50% rate of female births, find the probability that in 14 births, the number of girls is 13.
b. Assuming a 50% rate of female births, find the probability that in 14 births, the number of girls is 14.
c. Assuming a 50% rate of female births, find the probability that in 14 births, the number of girls is 13 or more.
d. Do these preliminary results suggest that the XSORT method is effective in increasing the likelihood of a baby being a girl? Explain.