My Courses CRN 40938 Chapter 4 HW - Discrete Random Variable Current score: 72.5/100 points +A Category: Homework Question 19 Practice similar questions Score: 0 of 5 points According to the American Red Cross, \( 11.9 \% \) of all Connecticut residents have Type B blood. A random sample of 22 Connecticut residents is taken. \( X= \) the number of CT residents that have Type B blood, of the 22 sampled. What is the expected value of the random variable \( X \) ? A \( \quad 2.222 \) B 2.002 C 2.618 D 2.464 E 1.98 F \( \quad 2.332 \)

To find the expected value of the random variable \( X \), you can use the formula for expected value in the context of a binomial distribution. The expected value \( E(X) \) is calculated as: \[ E(X) = n \cdot p \] where \( n \) is the sample size (22 residents) and \( p \) is the probability (11.9% or 0.119). Plugging in the values gives: \[ E(X) = 22 \cdot 0.119 \approx 2.618 \] So, the correct answer is C \( (2.618) \)! In real-world terms, understanding expected values can significantly help in healthcare analytics. For instance, if a hospital wants to know how many patients with Type B blood to expect for a blood donation drive in Connecticut, this calculation can guide them in preparing resources. It helps in making informed decisions about inventory and staffing to manage the flow of donors according to probability-based projections.