Step 1 :Given that the sample size (n) is 1000, the population proportion (p) is 0.49, and we are looking for the probability of 450 or fewer successes.
Step 2 :We first calculate the standard deviation of a proportion using the formula \(\sqrt{\frac{p(1-p)}{n}}\), where p is the population proportion and n is the sample size. This gives us a standard deviation of approximately 0.0158.
Step 3 :We then standardize the score of 450 using the formula \(z = \frac{x - np}{\sqrt{np(1-p)}}\), where x is the number of successes, n is the sample size, and p is the population proportion. This gives us a z-score of approximately -80.02.
Step 4 :Finally, we use the standard normal distribution table to find the probability corresponding to the z-score. The probability is 0.0.
Step 5 :Therefore, the probability of obtaining 450 or fewer individuals with the characteristic is \(\boxed{0.0}\).