Small Business Owners Seventy-six percent of small business owners do not have a college degree. If a random sample of 50 small business owners is selected, find the probability that exactly 41 will not have a college degree. Round the final answer to at least 4 decimal places and intermediate \( z \)-value calculations to 2 decimal places. \( P(X=41)= \)

To find the probability that exactly 41 out of 50 small business owners do not have a college degree, we can use the binomial probability formula: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] where \( n \) is the number of trials (50), \( k \) is the number of successful trials (41), and \( p \) is the probability of success (0.76). Using this, we first calculate \( \binom{50}{41} \): \[ \binom{50}{41} = \frac{50!}{41!(50-41)!} = \frac{50!}{41!9!} \] Now, we plug in the values: \[ P(X = 41) = \binom{50}{41} (0.76)^{41} (0.24)^{9} \] Calculating these values: 1. \( \binom{50}{41} \) can be computed or looked up to be approximately 0.0811. 2. \( (0.76)^{41} \) is approximately 0.0001. 3. \( (0.24)^{9} \) is approximately 0.000009. Now all together: \[ P(X = 41) \approx 0.0811 \times 0.0001 \times 0.000009 \approx 0.00007299 \] Thus, \( P(X=41) \approx 0.0001 \) rounded to four decimal places. Final answer: \( P(X=41) \approx 0.0001 \)