Fill in the Blank 4 points For a uniform random variable \( X \sim U(18,26) \), find the following probabilities. State answers as decimals. \( P(X<24)= \) type your answer... \( P(X \geq 24)= \) type your answer... \( P(19.5 \leq X \leq 24.0)= \) type your answer... \( P(X=22.22)= \) type your answer...

For a uniform random variable \( X \sim U(18,26) \), we know that the probability density function is constant within the bounds of the distribution. First, let's calculate each required probability: 1. To find \( P(X < 24) \): \[ P(X < 24) = \frac{24 - 18}{26 - 18} = \frac{6}{8} = 0.75 \] 2. For \( P(X \geq 24) \): \[ P(X \geq 24) = 1 - P(X < 24) = 1 - 0.75 = 0.25 \] 3. To calculate \( P(19.5 \leq X \leq 24.0) \): \[ P(19.5 \leq X \leq 24.0) = \frac{24 - 19.5}{26 - 18} = \frac{4.5}{8} = 0.5625 \] 4. Since \( X \) is continuous, \( P(X = 22.22) = 0 \). Putting it all together: - \( P(X < 24) = 0.75 \) - \( P(X \geq 24) = 0.25 \) - \( P(19.5 \leq X \leq 24.0) = 0.5625 \) - \( P(X = 22.22) = 0 \)