**4. Correct. The
answer is false**

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.