Final answer:
The probability that the average height in a random sample of chief executive officers exceeds 69 inches can be calculated using the normal distribution; however, the population mean and standard deviation are needed to provide an answer.
Step-by-step explanation:
To determine how likely it is that the average height in a random sample of 100 chief executive officers exceeds 69 inches, we need to use the concept of the sampling distribution of the sample mean, typically applied in inferential statistics. Assuming we know the population mean and the population standard deviation, we can use the normal distribution to calculate this probability.
However, the student's question is missing some key details, such as the population mean and standard deviation for the heights of chief executive officers. In general, if we had these values and given the large sample size of 100, we might apply the Central Limit Theorem, which states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases. With the mean (μ) and standard deviation (σ) of the population, we can compute the standard error of the mean (σ/√n), where n is the sample size. Subsequently, we could use a z-score to find the probability that the mean height exceeds 69 inches.
Without this information, however, we cannot provide a numerical answer. Thus, to answer the original question, information about the population mean and standard deviation of CEO heights is required.