Final answer:
To find the approximate probability that a random sample of 300 candies will contain 20% or more orange candies, we can use a normal approximation. The probability is approximately 0.1126.
Step-by-step explanation:
To find the approximate probability that a random sample of 300 candies will contain 20% or more orange candies, we can use a normal approximation. First, we need to calculate the expected number of orange candies in the sample. Since the packages contain 17% orange candies, we can expect 0.17 * 300 = 51 orange candies in the sample.
Next, we need to calculate the standard deviation of the sample proportion. The formula for standard deviation of a sample proportion is sqrt((p(1-p))/n), where p is the population proportion and n is the sample size. Plugging in the values, we get sqrt((0.17(1-0.17))/300) = 0.0247.
Finally, we can use the normal distribution to find the probability that at least 20% of the candies in the sample are orange. We can standardize the proportion using the formula (x - p) / standard deviation, where x is the desired proportion. In this case, x = 0.20. Plugging in the values, we get (0.20 - 0.17) / 0.0247 = 1.214. We can then use a standard normal table or calculator to find the probability associated with this z-score, which is approximately 0.1126.