4. Incorrect. The answer is false, not true.

To answer this question, it is necessary to calculate the probability distribution function of T.

P[T=0.1] = P[30 < X < 35] = P[(30-33)/3 < (X - μ)/σ < (35-33)/3]

P[T=0.1] = ϕ(0.67) - ϕ(-1) = 0.7486 - 0.1587 = 0.5899.

ϕ( ) is the standard normal distribution. To calculate the probabilities, it is necessary to check the tables for this distribution.

P[T=0.05] = P[(35 ≤ X < 40) U (25 < X ≤ 30)]

P[T=0.05] = P[(35-33)/3 < (X - μ)/σ < (40-33)/3] + P[(25-33)/3 < (X - μ)/σ < (30-33)/3]

P[T=0.05] = ϕ(2.33) - ϕ(0.67) + ϕ(-1) - ϕ(-2.67) = 0.3964

P[T=-0.10] = 1 - (0.5899 + 0.3964) = 0.0137

The probability distribution function of T is expressed in the following table:

t	0.10	0.05	-0.10
P[T=t]	0.5899	0.3964	0.0137

Therefore, E[T] = (0.10)*(0.5899) + (0.05)*(0.3964) – (0.10)*(0.0137) = 0.0774.