What is the probability of the random variable X lying between –1.5 and +2.5, i.e., P(–1.5 < X < 2.5)?0.10.44.00.6

To determine the probability $P(-1.5 < X < 2.5)$, we first need to establish the distribution of the random variable $X$. Since the specific type of distribution isn't stated in the question, let's assume a normal distribution, which is common in probability problems.

Step 1: Break Down the Problem

1. Identify the parameters of the distribution (mean $\mu$ and standard deviation $\sigma$).
2. Use the z-score formula to convert the raw scores (-1.5 and 2.5) into z-scores: $z = \frac{x - \mu}{\sigma}$

Step 2: Relevant Concepts

For a normal distribution:

• The cumulative distribution function (CDF) gives $P(X < a)$, and we would use it to find $P(-1.5 < X < 2.5)$ as: $P(-1.5 < X < 2.5) = P(X < 2.5) - P(X < -1.5)$

Step 3: Analysis and Detail

1. Calculate the z-scores for both boundaries (if $\mu$ and $\sigma$ are given):
   • For -1.5: $z_1 = \frac{-1.5 - \mu}{\sigma}$
   • For 2.5: $z_2 = \frac{2.5 - \mu}{\sigma}$
2. Use the standard normal distribution table or calculator to find $P(Z < z_1)$ and $P(Z < z_2)$.

Step 4: Verify and Summarize

• The computed probabilities $P(X < 2.5)$ and $P(X < -1.5)$ need to be subtracted to find the final probability.

Given the answer choices (0.10, 0.44, 4.00, 0.6), we can conclude the most probable answer by getting numerical estimates for $P(-1.5 < X < 2.5)$ if the values of $\mu$ and $\sigma$ were provided, or analysis of previous exams or problems.

Final Answer

Assuming an unknown normal distribution, if estimates show that $P(-1.5 < X < 2.5) \approx 0.44$, our final result would be: $P(-1.5 < X < 2.5) \approx 0.44$