The height of adult males on a given South Pacific Island is approximately normally distributed with mean 63 inches and standard deviation of 4 inches. What percentage of the adult male population on this island is:
a. Taller then 65 inches
To solve this problem, we can use the standard normal distribution formula:
z = (x - μ) / σ
where z is the z-score, x is the value we are interested in (65 inches), μ is the mean (63 inches), and σ is the standard deviation (4 inches).
Plugging in the numbers, we get:
z = (65 - 63) / 4 = 0.5
Using a standard normal distribution table or calculator, we can find the percentage of the population that is taller than 65 inches by looking up the area to the right of the z-score of 0.5. This area is approximately 30.85%.
Therefore, about 30.85% of the adult male population on this island is taller than 65 inches.
To find the percentage of the adult male population on this island that is taller than 65 inches, we need to calculate the standard score (z-score) for this value using the formula:
z = (x - μ) / σ
where x is the value we want to find the percentage for, μ is the mean of the distribution, and σ is the standard deviation.
Plugging in the values:
z = (65 - 63) / 4
z = 2 / 4
z = 0.5
The next step is to find the cumulative probability associated with this z-score. We can look up this value in a standard normal distribution table or use a calculator.
Using a standard normal distribution table, we find that the cumulative probability for a z-score of 0.5 is approximately 0.6915.
To convert this to a percentage, we multiply by 100:
0.6915 * 100 = 69.15%
Therefore, approximately 69.15% of the adult male population on this island is taller than 65 inches.