Find the normal approximation for the binomial probability that x=5, where n=14 and p= 0.3.

Compare this probability to the value of p(x=5) found in Table 2 of Appendix

X~B(14, 0.3)

Let Y~(μ,σ²), where
μ = 14 * 0.4 = 4.2
σ² = 2.94
σ = 1.715

P(X=5) = P(4.5 < Y < 5.5)
= P((4.5−4.2)/1.715 < Z < (5.5−4.2)/1.715)
= P(0.17 < Z < 0.76)
= P(Z < 0.76) − P(Z < 0.17)
= 0.7764 − 0.5675
= 0.2089

I don't have Appendix you mention, but I can calculate binomial probability using calculator:

P(X = 5)
= C(14,5) (0.3)^5 (0.7)^9
= 0.1963