A sample of size n taken from a population with mean = µ and standard deviation = σ has sample mean = µ and sample s.d. = σ/√n.
If the final exam scores are normally distributed, and X is a random variable for the mean of a sample, then
Pr[X < 70] = Pr[(X - 73) / (7.8/√24) < (70 - 73) / (7.8/√24)]
… ≈ Pr[Z < -1.8842]
… ≈ 0.0298
(where Z is normally distributed with µ = 0 and σ = 1).
