Final answer:
The normal approximation can be used to estimate the probability that less than 30% of the freshmen in the sample are planning to major in Science, under certain conditions. The conditions include having a large sample size and an approximately normal sampling distribution. The mean and standard deviation of the sampling distribution can be used to calculate the probability using the normal distribution.
Step-by-step explanation:
The normal approximation can be used to find the probability that less than 30% of the freshmen in the sample are planning to major in Science if certain conditions are met. The normal approximation relies on the Central Limit Theorem, which states that the sampling distribution of a large sample size will be approximately normal, regardless of the shape of the population distribution. In this case, the sample size should ideally be larger than 30 and the sampling distribution should be approximately normal. If these conditions are met, the normal approximation can be used to estimate the probability.
Let's assume the sample size is large and the sampling distribution is approximately normal. We can use the normal distribution to estimate the probability. To do this, we need to find the mean and standard deviation of the sampling distribution. The mean of the sampling distribution is the same as the population proportion, which is 30% in this case. The standard deviation of the sampling distribution, also known as the standard error, is calculated using the formula: Standard Error = sqrt((p * (1-p))/n), where p is the population proportion and n is the sample size. Once we have the mean and standard deviation of the sampling distribution, we can use the normal distribution to find the probability that less than 30% of the freshmen in the sample are planning to major in Science.