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. under 59 inches
To find the percentage of the adult male population that is under 59 inches, we need to calculate the z-score for 59 inches:
z = (59 - 63) / 4 = -1
Using a standard normal distribution table or calculator, we can find that the proportion of the population below this z-score is approximately 0.1587, or 15.87%. Therefore, about 15.87% of the adult male population on the island is under 59 inches tall.
To find the percentage of the adult male population on this island that is under 59 inches, we need to find the z-score corresponding to this height and then look up the area under the normal curve to the left of that z-score.
The formula for calculating the z-score is:
z = (x - μ) / σ
where:
x is the value (59 inches in this case)
μ is the mean (63 inches)
σ is the standard deviation (4 inches)
Substituting the values into the formula, we get:
z = (59 - 63) / 4
z = -4 / 4
z = -1
Now, we need to look up the area to the left of a z-score of -1 in the standard normal distribution table or using a calculator.
The area to the left of z = -1 is approximately 0.1587, or 15.87%.
Therefore, approximately 15.87% of the adult male population on this South Pacific Island is under 59 inches.