According to the American Red Cross, 10.1% of all Connecticut residents have Type B blood. A random sample of 19 Connecticut residents is taken.

the number of CT residents that have Type B blood, of the 19 sampled.

What is the expected value of the random variable ?

1.672

2.166

2.242

1.71

1.919

1.539

To solve this, we use the **binomial distribution** because we are dealing with a fixed number of trials (19 Connecticut residents), and each trial has two possible outcomes: either a resident has Type B blood or they don't.

The expected value \( E(X) \) for a binomial distribution is given by:

\[
E(X) = n \cdot p
\]

Where:
- \( n \) is the number of trials (in this case, 19),
- \( p \) is the probability of success (in this case, the probability that a resident has Type B blood, which is 0.101).

Substituting the values:

\[
E(X) = 19 \cdot 0.101 = 1.919
\]

Thus, the expected value of the random variable is **1.919**.

Do you want more details or have any questions?

Here are 5 related questions to further your understanding:
1. What is the variance of this binomial distribution?
2. How would the expected value change if the sample size increased to 50?
3. What is the probability that exactly 2 residents out of 19 have Type B blood?
4. How does the binomial distribution differ from the normal distribution?
5. If the probability were 15% instead of 10.1%, what would be the new expected value?

**Tip**: The binomial distribution assumes that the probability of success remains constant across all trials.

According to the American Red Cross, 10.1% of all Connecticut residents have Type B blood. A random sample of 19 Connecticut residents is taken. What is the expected value of the random variable?

Calculate the expected value of the random variable for a binomial distribution with a 10.1% probability that a Connecticut resident has Type B blood, and a sample size of 19. Suitable for high school students in Grades 10-12.

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