a. Calculate Pr(X < 23000) and multiply the answer by 100.
I get approximately 26.38%.
b. Calculate Pr(21250 < X < 23750) and multiply the answer by 100.
I get approximately 24.98%.
Without knowing how you've been taught to calculate such probabilities (using tables, technology such as TI-84 or TI-89 calculators, numerical integration of the pdf etc.) it's impossible to provide further relevant help.
a. Calculate Pr(X > 111.8)
I get 0.3897 (correct to four decimal places).
Let Y be the random variable number of years out of 40 randomly picked years that X > 111.8.
Then Y ~ Binomial(n = 40, p = 0.3897).
You need to calculate Pr(Y = 40) ......
b. Proceed similar to part a. Calculate Pr(105 < X < 112) etc.