Assume that a researcher randomly selects 14 newborn babies and counts the number of girls​ selected, x. the probabilities corresponding to the 14 possible values of x are summarized in the given table. find the probability of selecting exactly 4 girls..

The number of girls in the 14 newborn babies selected is a binomially distributed random variable with n = 14 and p = 0.5. And we know that the binomial probability distribution is given by 

P(X = k) = (nCk) p^k (1–p)^(n-k)

So, P(X = 0) = (14C0) • 0.5^0 • (1–0.5)^(14-0) = 0.000

P(X = 1) = (14C1) • 0.5^1 • (1–0.5)^(14–1) = 0.001

And so on.

Thus, P(X = 4) = (14C4) • 0.5^(4 • (1–0.5)^(14–4) = 0.061

So the probability of selecting exactly 4 girls is 0.061.