Suppose that the heights of adult men in the United States are normally distributed with a mean of inches and a standard deviation of inches. What proportion of the adult men in United States are more than feet tall? (Hint: feet inches.) Round your answer to at least four decimal places.
Your values are not given.
Z = (score-mean)/SD
Use your values to find the Z score.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score.
To find the proportion of adult men in the United States who are more than a certain height, we can use the z-score and the standard normal distribution.
First, let's convert the height of feet to inches. Since there are 12 inches in a foot, we have: 6 feet * 12 inches/foot = 72 inches.
Next, we need to calculate the z-score for 72 inches using the formula:
z = (x - μ) / σ
where x is the height (72 inches), μ is the mean height, and σ is the standard deviation.
Since the mean height and standard deviation are not given in the question, we cannot calculate the z-score directly. Without this information, it is not possible to determine the proportion of men who are more than 72 inches tall.
To find the proportion of adult men in the United States who are more than a certain height, we need to calculate the z-score and then use a standard normal distribution table.
Let's first convert feet into inches. Since there are 12 inches in a foot, feet is equal to inches. So, we need to find the proportion of men who are more than inches tall.
To calculate the z-score, we use the formula:
z = (x - μ) / σ
where:
- x is the value we want to convert to a z-score (in this case, inches),
- μ is the mean of the normal distribution (unknown in this case),
- σ is the standard deviation of the normal distribution.
We're given that the mean of the normal distribution is inches and the standard deviation is inches.
Using the formula, the z-score is:
z = ( - ) /
Next, we need to use a standard normal distribution table or a calculator to find the proportion of men with a z-score greater than .
Assuming that the mean and standard deviation are known, you can substitute the actual values into the z-score formula and use a standard normal distribution table or calculator to find the proportion of the population greater than that z-score.
Please provide the values for the mean and standard deviation so we can continue the calculation.