Final answer:
To find the probability of obtaining a mean height of 65 inches or higher in a sample of 30 adult women, we can use the Central Limit Theorem and the z-score formula.
Step-by-step explanation:
To find the probability of obtaining a mean height of 65 inches or higher in a sample of 30 adult women, we need to use the Central Limit Theorem. The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.
In this case, we assume that the heights of adult women in the population are normally distributed with a mean of mu and a standard deviation of sigma. Since the sample size is large (n = 30), we can use the z-score formula to standardize the sample mean and calculate the probability.
The z-score formula is: z = (x - mu) / (sigma / sqrt(n)), where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.
In this case, we want to find the probability of obtaining a sample mean height of 65 inches or higher. Assuming a population mean of mu and a population standard deviation of sigma, we can calculate the z-score and use a standard normal distribution table (or a calculator) to find the probability.