We want to find the sample size n such that
Pr[|µ - 101| < 5] = 0.98
where µ is ... some mean. It can be the mean for either the true population or the sample. It's unclear which is which from the given info, but that's not actually important.
In the inequality, divide both sides by the standard error, σ/√n = 16/√n :
Pr[|µ - 101|/(16/√n) < 5/(16/√n)] = 0.98
Use a lookup table to find the z-score corresponding to 0.98 :
⇒ 5/(16/√n) ≈ 2.05375
Solve for n :
⇒ n ≈ 43.1911 ≈ 44
