According to the American Red Cross, 11.5% of all Connecticut residents have Type B blood. A random sample of 17 Connecticut residents is taken.

the number of CT residents that have Type B blood, of the 17 sampled.

What is the standard deviation of the random variable ?

This problem is modeled by a **binomial distribution** because there are two possible outcomes: either a person has Type B blood or they don't. The number of Connecticut residents with Type B blood in a sample of 17 is a binomial random variable.

The standard deviation for a binomial distribution is given by the formula:

\[
\sigma = \sqrt{n \cdot p \cdot (1 - p)}
\]

where:
- \( n \) is the number of trials (in this case, the sample size, 17),
- \( p \) is the probability of success (the probability of having Type B blood, 11.5% or 0.115),
- \( 1 - p \) is the probability of failure (not having Type B blood, 88.5% or 0.885).

Let’s calculate the standard deviation.

\[
\sigma = \sqrt{17 \cdot 0.115 \cdot 0.885}
\] 

Now, I'll compute the result.The standard deviation of the random variable, which represents the number of Connecticut residents with Type B blood in a sample of 17, is approximately **1.32**.

Would you like more details on this calculation or further explanation?

Here are 5 related questions to think about:
1. What is the mean of the binomial distribution in this case?
2. How does increasing the sample size affect the standard deviation?
3. What would be the probability that exactly 3 people in the sample have Type B blood?
4. How would the standard deviation change if the probability of Type B blood were 20% instead of 11.5%?
5. What assumptions underlie the use of a binomial distribution for this problem?

**Tip:** The square root of a binomial distribution's variance is often a key indicator of how spread out the outcomes are from the mean.

According to the American Red Cross, 11.5% of all Connecticut residents have Type B blood. A random sample of 17 Connecticut residents is taken. What is the standard deviation of the random variable?

Learn how to calculate the standard deviation of a binomial distribution using a sample of Connecticut residents with Type B blood. This problem uses the binomial distribution formula and is ideal for students in Grades 10-12. Understand key concepts like probability and standard deviation through a practical example.

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