Questions: Coronary bypass surgery: A healthcare research agency reported that 46% of people who had coronary bypass surgery in 2008 were over the age of 65. Twelve coronary bypass patients are sampled. Part 1 of 2 (a) What is the mean number of people over the age of 65 in a sample of 12 coronary bypass patients? Round the answer to two decimal places. The mean number of people over the age of 65 is 1. Part 2 of 2 (b) What is the standard deviation of the number of people over the age of 65 in a sample of 12 coronary bypass patients? Round the answer to four decimal places. The standard deviation of the number of people over the age of 65 is .

Solution Steps

To find the mean number of people over the age of 65 in a sample of 12 coronary bypass patients, we use the formula for the mean of a binomial distribution:

\[ \mu = n \cdot p \]

where:

• \( n = 12 \) (the number of trials),
• \( p = 0.46 \) (the probability of success).

Calculating this gives:

\[ \mu = 12 \cdot 0.46 = 5.52 \]

Thus, the mean number of people over the age of 65 is \( 5.52 \).

Next, we calculate the standard deviation using the formula:

\[ \sigma = \sqrt{n \cdot p \cdot q} \]

where:

• \( q = 1 - p = 0.54 \) (the probability of failure).

Calculating the variance first:

\[ \sigma^2 = n \cdot p \cdot q = 12 \cdot 0.46 \cdot 0.54 = 2.9808 \]

Now, taking the square root to find the standard deviation:

\[ \sigma = \sqrt{2.9808} \approx 1.7265 \]

Thus, the standard deviation of the number of people over the age of 65 is \( 1.7265 \).

Final Answer