Final answer:
To find the height of the tallest 1% of people, we can use the standard normal distribution and calculate the corresponding z-score. Then, we can use the formula for standardizing a value to find the actual height.
Step-by-step explanation:
To find out how many inches tall the tallest 1% of people are, we need to find the z-score associated with the cutoff point of the top 1% of the standard normal distribution. The z-score represents the number of standard deviations a value is from the mean. In this case, we want to find the z-score that corresponds to a cumulative probability of 0.99, since we are interested in the top 1%. Using a standard normal distribution table or a calculator, we find that the z-score is approximately 2.33.
Next, we can use the formula for standardizing a value using the z-score: z = (X - mean) / standard deviation. Since we are looking for the tallest 1% of people, we want to find the height that corresponds to a z-score of 2.33. Plugging in the values, we have 2.33 = (X - 68) / 4. Solving for X, we get X = 2.33 * 4 + 68.