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.
find the z-score:
z=(x-mu)/sigma
where mu= mean and sigma=standard deviation
after you find the z-score, you need to look at the z-score chart for the proportion
http://www.thebeststatistics.info/sta/table_zvals.html
To find the proportion of adult men in the United States who are more than a certain height, we need to calculate the area under the normal distribution curve to the right of that height.
In this case, the given height is 6 feet, which is equivalent to 6 * 12 = 72 inches.
To calculate the proportion, we need to standardize the height using the formula:
Z = (X - μ) / σ
where X is the given height, μ is the mean, and σ is the standard deviation.
For this problem, the mean (μ) and standard deviation (σ) are not provided, so we cannot proceed without that information.
To find the proportion of adult men in the United States who are more than a certain height, we will need to use the standard normal distribution.
Step 1: Convert the given height from feet to inches.
Since 1 foot is equal to 12 inches, we need to convert the given height of " feet" into inches.
" feet" is equal to * 12 inches = inches.
Step 2: Standardize the given height.
To use the standard normal distribution, we need to standardize the given height by subtracting the mean and dividing by the standard deviation.
Standardized height = (height - mean) / standard deviation.
In this case,
Standardized height = ( - ) /
Step 3: Find the proportion using the standard normal distribution table.
We need to find the proportion of adult men with a height greater than the standardized height obtained in Step 2. This can be found using the standard normal distribution table or calculator.
Let's assume the standardized height obtained in Step 2 is "Z".
We need to find P(Z > ).
Using a standard normal distribution table or calculator:
P(Z > ) ≈
Remember to round the answer to at least four decimal places.
Step 4: Substitute the values back into the original problem.
Since we have converted the given height to inches, calculate the required proportion of adult men in the United States who are more than " feet" tall by substituting the obtained value from Step 3:
Proportion =
Make sure to round the answer to at least four decimal places.