1. The problem asks for the probability that a standard normal variable $Z$ lies between $-2.59$ and $1.47$, i.e., $P(-2.59 < Z < 1.47)$. 2. For a standard normal distribution, probabilities are found using the cumulative distribution function (CDF) $\Phi(z)$, which gives $P(Z \leq z)$. 3. The probability between two values $a$ and $b$ is $P(a < Z < b) = \Phi(b) - \Phi(a)$. 4. Using standard normal tables or a calculator, find: - $\Phi(1.47) \approx 0.9292$ - $\Phi(-2.59) \approx 0.0048$ 5. Calculate the probability: $$P(-2.59 < Z < 1.47) = 0.9292 - 0.0048 = 0.9244$$ 6. Therefore, the value of $P(-2.59 < Z < 1.47)$ is approximately $0.9244$. This means there is about a 92.44% chance that $Z$ falls between $-2.59$ and $1.47$.