P(X ≤ 65) = P((X - 79)/7 ≤ (65 - 79)/7) = P(Z ≤ -2)
where Z follows the standard normal distribution with mean 0 and standard deviation 1.
Recall that for any normal distribution with mean µ and s.d. σ, we have
P(|X - µ| ≤ 2σ) ≈ 0.95
which in the case of Z translates to
P(-2 ≤ Z ≤ 2) ≈ 0.95
Now,
P(-2 ≤ Z) + P(-2 ≤ Z ≤ 2) + P(Z ≥ 2) = 1
==> P(-2 ≤ Z) + P(Z ≥ 2) ≈ 0.05
Any normal distribution is symmetric about its mean, so P(-2 ≤ Z) = P(Z ≥ 2), and this gives us
==> 2 P(-2 ≤ Z) ≈ 0.05
==> P(-2 ≤ Z) ≈ 0.025
