Question

In a recent survey, 80% of the community favored building a health center in their neighborhood. If 15 citizens are chosen, what is the standard deviation of the number favoring the health center?

Answer 1

To find the standard deviation, calculate the variance using the formula npq, where n is the number of trials and p is the probability of success. Then take the square root of the variance.

Step-by-step explanation:

To find the standard deviation of the number of citizens favoring the health center, you need to calculate the variance first. The variance of a binomial distribution is given by the formula npq, where n is the number of trials and p is the probability of success.

In this case, the probability of favoring the health center is 80%, so p = 0.8. The number of trials is 15, so n = 15. Now calculate npq: 15 x 0.8 x (1-0.8) = 15 x 0.8 x 0.2 = 2.4.

Finally, take the square root of the variance to find the standard deviation: √2.4 = 1.549.

Answer 2

The standard deviation of the number of citizens favoring the health center out of 15 chosen is approximately 1.55, calculated using the binomial distribution with a probability of 80% favorability.

Step-by-step explanation:

To calculate the standard deviation of the number favoring the health center when 15 citizens are chosen, we can treat this as a binomial distribution problem. In the survey, with an 80% favorability rate, the probability of a citizen favoring the health center (p) is 0.8, and the probability of a citizen not favoring it (q) is 1 - p, which equals 0.2.

The formula for the standard deviation (σ) of a binomial distribution is σ = √(npq), where n is the number of trials (in this case, the number of citizens chosen), p is the probability of success (favoring the health center), and q is the probability of failure (not favoring the health center).

Substituting the given values into the formula:

• n = 15 (number of chosen citizens)
• p = 0.8 (probability of favoring the center)
• q = 0.2 (probability of not favoring the center)

We calculate the standard deviation as follows:

σ = √(15 * 0.8 * 0.2) = √(2.4) ≈ 1.5492

Therefore, the standard deviation of the number of citizens favoring the health center out of 15 chosen is approximately 1.55.