Questions: Fifty-seven percent of families say that their children have an influence on their vacation plans. Consider a sample of eight families who are asked if their children influence their vacation plans. What is the probability that exactly three families say that their children have an influence on their vacation plans.

Solution Steps

To find the standard deviation of the number of houses burglarized, we use the formulas for mean, variance, and standard deviation in a binomial distribution:

• Mean \( \mu = n \cdot p = 20 \cdot 0.10 = 2.0 \)
• Variance \( \sigma^2 = n \cdot p \cdot q = 20 \cdot 0.10 \cdot 0.90 = 1.8 \)
• Standard Deviation \( \sigma = \sqrt{npq} = \sqrt{20 \cdot 0.10 \cdot 0.90} \approx 1.342 \)

Thus, the standard deviation of the number of houses burglarized is \( \sigma \approx 1.342 \).

For the second question, we need to determine the probability that exactly three families say their children influence their vacation plans. The probability of success \( p \) is given as:

• Probability of success \( p = 0.57 \)

Final Answer