In this problem exponential random variable X represents the physical examination time. Also, the mean μ = 25 minutes of the physical examination time, therefore

λ=1= 1 =0.04μ 25

The probability density function is as follows,
f (x) = (0.04) e-0.04x, x ≥ 0

Therefore X ~ Exponential (λ = 0.04) and to find the probability that the physical exam duration takes less than 20 minutes P (X < 20).

P(X<20)= ∫20=(0.04)e−0.04xdx=−e−0.04x 20 =−(e−0.8 −1)=0.5500